From 1bcae8faa08e4e1fdbaf6c2cbd2fcdf365b697ce Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Fri, 29 Aug 2025 09:03:32 -0400 Subject: [PATCH 1/8] initial slides --- class02/ISYE_8803___Lecture_2___Slides.pdf | Bin 0 -> 270297 bytes class02/SQP.tex | 123 +++++++++ class02/eq_constraints.tex | 157 +++++++++++ class02/ineq_constraints.tex | 303 +++++++++++++++++++++ class02/intro.tex | 63 +++++ class02/main.tex | 82 ++++++ class02/notation.tex | 33 +++ class02/root_finding.tex | 156 +++++++++++ 8 files changed, 917 insertions(+) create mode 100644 class02/ISYE_8803___Lecture_2___Slides.pdf create mode 100644 class02/SQP.tex create mode 100644 class02/eq_constraints.tex create mode 100644 class02/ineq_constraints.tex create mode 100644 class02/intro.tex create mode 100644 class02/main.tex create mode 100644 class02/notation.tex create mode 100644 class02/root_finding.tex diff --git a/class02/ISYE_8803___Lecture_2___Slides.pdf b/class02/ISYE_8803___Lecture_2___Slides.pdf new file mode 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Lagrangian/objective. + \item Each iteration: solve a QP to get a step \(d\), update \(x \leftarrow x + \alpha d\). + \item Strength: strong local convergence (often superlinear) with good Hessian info. +\end{itemize} +\end{frame} + +% ------------------------------------------------ +\begin{frame}{Target Problem (NLP)} +\[ +\min_{x \in \R^n} \ f(x) +\quad +\text{s.t.}\quad +g(x)=0,\quad h(x)\le 0 +\] +\begin{itemize} + \item \(f:\R^n\!\to\!\R\), \(g:\R^n\!\to\!\R^{m}\) (equalities), \(h:\R^n\!\to\!\R^{p}\) (inequalities). + \item KKT recap (at candidate optimum \(x^\star\)): +\[ +\exists \ \lambda \in \R^{m},\ \mu \in \R^{p}_{\ge 0}: +\ \grad f(x^\star) + \nabla g(x^\star)^T\lambda + \nabla h(x^\star)^T \mu = 0, +\] +\[ +g(x^\star)=0,\quad h(x^\star)\le 0,\quad \mu \ge 0,\quad \mu \odot h(x^\star) = 0. +\] +\end{itemize} +\end{frame} + +% ------------------------------------------------ +\begin{frame}{From NLP to a QP (Local Model)} +At iterate \(x_k\) with multipliers \((\lambda_k,\mu_k)\):\\[4pt] +\textbf{Quadratic model of the Lagrangian} +\[ +m_k(d) = \ip{\grad f(x_k)}{d} + \tfrac{1}{2} d^T B_k d +\] +with \(B_k \approx \nabla^2_{xx}\Lag(x_k,\lambda_k,\mu_k)\).\\[6pt] +\textbf{Linearized constraints} +\[ +g(x_k) + \nabla g(x_k)\, d = 0,\qquad +h(x_k) + \nabla h(x_k)\, d \le 0. +\] +\end{frame} + +% ------------------------------------------------ +\begin{frame}{The SQP Subproblem (QP)} +\[ +\begin{aligned} +\min_{d \in \R^n}\quad & \grad f(x_k)^T d + \tfrac{1}{2} d^T B_k d \\ +\text{s.t.}\quad & \nabla g(x_k)\, d + g(x_k) = 0, \\ +& \nabla h(x_k)\, d + h(x_k) \le 0. +\end{aligned} +\] +\begin{itemize} + \item Solve QP \(\Rightarrow\) step \(d_k\) and updated multipliers \((\lambda_{k+1},\mu_{k+1})\). + \item Update \(x_{k+1} = x_k + \alpha_k d_k\) (line search or trust-region). +\end{itemize} +\end{frame} + +% ------------------------------------------------ +\begin{frame}{Algorithm Sketch (SQP)} +\begin{enumerate} + \item Start with \(x_0\), multipliers \((\lambda_0,\mu_0)\), and \(B_0 \succ 0\). + \item Build QP at \(x_k\) with \(B_k\), linearized constraints. + \item Solve QP \(\Rightarrow\) get \(d_k\), \((\lambda_{k+1},\mu_{k+1})\). + \item Globalize: line search on merit or use filter/TR to choose \(\alpha_k\). + \item Update \(x_{k+1} = x_k + \alpha_k d_k\), update \(B_{k+1}\) (e.g., BFGS). +\end{enumerate} +\end{frame} + +% ------------------------------------------------ +\begin{frame}{Toy Example (Local Models)} +\textbf{Problem:} +\[ +\min_{x\in\R^2} \ \tfrac{1}{2}\norm{x}^2 +\quad \text{s.t.} \quad g(x)=x_1^2 + x_2 - 1 = 0,\ \ h(x)=x_2 - 0.2 \le 0. +\] +At \(x_k\), build QP with +\[ +\grad f(x_k)=x_k,\quad B_k=I,\quad +\nabla g(x_k) = \begin{bmatrix} 2x_{k,1} & 1 \end{bmatrix},\ +\nabla h(x_k) = \begin{bmatrix} 0 & 1 \end{bmatrix}. +\] +Solve for \(d_k\), then \(x_{k+1}=x_k+\alpha_k d_k\). +\end{frame} + + +% ------------------------------------------------ +\begin{frame}{Globalization: Making SQP Robust} +SQP is an important method, and there are many issues to be considered to obtain an \textbf{efficient} and \textbf{reliable} implementation: +\begin{itemize} + \item Efficient solution of the linear systems at each Newton Iteration (Matrix block structure can be exploited. + \item Quasi-Newton approximations to the Hessian. + \item Trust region, line search, etc. to improve robustnes (i.e TR: restrict \(\norm{d}\) to maintain model validity.) + \item Treatment of constraints (equality and inequality) during the iterative process. + \item Selection of good starting guess for $\lambda$. +\end{itemize} +\end{frame} + + + + + + +% ------------------------------------------------ +\begin{frame}{Final Takeaways on SQP} +\textbf{When SQP vs.\ Interior-Point?} +\begin{itemize} + \item \textbf{SQP}: strong local convergence; warm-start friendly; natural for NMPC. + \item \textbf{IPM}: very robust for large, strictly feasible problems; good for dense inequality sets. + \item In practice: both are valuable—choose to match problem structure and runtime needs. +\end{itemize} +\textbf{Takeaways of SQP} +\begin{itemize} + \item SQP = Newton-like method using a sequence of structured QPs. + \item Globalization (merit/filter/TR) makes it reliable from poor starts. + \item Excellent fit for control (NMPC/trajectory optimization) due to sparsity and warm starts. +\end{itemize} +\end{frame} diff --git a/class02/eq_constraints.tex b/class02/eq_constraints.tex new file mode 100644 index 0000000..010398c --- /dev/null +++ b/class02/eq_constraints.tex @@ -0,0 +1,157 @@ + +%\section{Part II -- Equality constraints: KKT, Newton vs. Gauss–Newton} +\section{Constrained Optimization} + +% ==== Equality constraints: KKT, Newton vs. Gauss–Newton ==== + +\begin{frame}{Equality-constrained minimization: geometry and conditions} +\textbf{Problem.}; $\min_{x\in\mathbb{R}^n} f(x)\quad \text{s.t.}\quad C(x)=0, C:\mathbb{R}^n\to\mathbb{R}^m$. + +\medskip +\textbf{Geometric picture.} At an optimum on the manifold $C(x)=0$, the negative gradient must lie in the tangent space: + +$$ +\grad f(x^\star)\ \perp\ \mathcal{T}_{x^\star}=\{p:\; J_C(x^\star)p=0\}. +$$ + +Equivalently, the gradient is a linear combination of constraint normals: + +$$ +\grad f(x^\star)+J_C(x^\star)^{\!T}\lambda^\star=0,\qquad C(x^\star)=0\quad(\lambda^\star\in\mathbb{R}^m). +$$ + +\medskip +\textbf{Lagrangian.}; $L(x,\lambda)=f(x)+\lambda^{\!T}C(x)$. +\end{frame} + +\begin{frame}{A nicer visual explanation/derivation of KKT conditions} +\begin{center} + Quick little whiteboard derivation +\end{center} + +\end{frame} + + + + + +\begin{frame}{KKT system for equalities (first-order necessary conditions)} +\textbf{KKT (FOC).} + +$$ +\grad_x L(x,\lambda)=\grad f(x)+J_C(x)^{\!T}\lambda=0,\qquad \grad_\lambda L(x,\lambda)=C(x)=0. +$$ + +\textbf{Solve by Newton on KKT:} linearize both optimality and feasibility: + +$$ +\begin{bmatrix} +\hess f(x) + \sum_{i=1}^m \lambda_i\,\hess C_i(x) & J_C(x)^{\!T}\\[2pt] +J_C(x) & 0 +\end{bmatrix} +\begin{bmatrix}\Delta x\\ \Delta\lambda\end{bmatrix} +=- +\begin{bmatrix} +\grad f(x)+J_C(x)^{\!T}\lambda\\ C(x) +\end{bmatrix}. +$$ + +\textit{Notes.} This is a symmetric \emph{saddle-point} system; typical solves use block elimination (Schur complement) or sparse factorizations. + + +\end{frame} + +\begin{frame}{Move to Julia Code} +\begin{center} + \textbf{Quick Demo of Julia Notebook: part2\_eq\_constraints.ipynb} +\end{center} +\end{frame} + +\begin{frame}{Numerical practice: Newton on KKT} +\textbf{When it works best.} +\begin{itemize} +\item Near a regular solution with $J_{C}(x^\star)$ full row rank and positive-definite reduced Hessian. +\item With a globalization (line search on a merit function) and mild regularization for robustness. +\end{itemize} + +\textbf{Common safeguards.} +\begin{itemize} +\item \emph{Regularize} the $(1,1)$ block to ensure a good search direction (e.g., add $\beta I$). +\item \emph{Merit/penalty} line search to balance feasibility vs.\ optimality during updates. +\item \emph{Scaling} constraints to improve conditioning of the KKT system. +\end{itemize} + + +\end{frame} + +\begin{frame}{Gauss--Newton vs.\ full Newton on KKT} +\textbf{Full Newton Hessian of the Lagrangian:} $\nabla_{xx}^2 L(x,\lambda) &= \hess f(x)+\sum_{i=1}^m \lambda_i\,\hess C_i(x)$ + +\textbf{Gauss--Newton approximation:} drop the \emph{constraint-curvature} term $\sum_i \lambda_i,\hess C_i(x)$: + +\begin{align*} +H_{\text{GN}}(x) &\approx \hess f(x). +\end{align*} + +\textbf{Trade-offs (high level).} +\begin{itemize} +\item \emph{Full Newton:} fewer iterations near the solution, but each step is costlier and can be less robust far from it. +\item \emph{Gauss--Newton:} cheaper per step and often more stable; may need more iterations but wins in wall-clock on many problems. +\end{itemize} + +\textbf{Practice tip.} Start with GN (with line search); switch to full Newton (or add low-rank updates) as feasibility improves. + + +\end{frame} + +% ==== Inequalities & KKT: complementarity ==== + +\begin{frame}{Inequality-constrained minimization and KKT} +\textbf{Problem.} $\quad \quad \min f(x)\quad\text{s.t.}\quad c(x)\ge 0, \quad \quad c:\mathbb{R}^n\to\mathbb{R}^p$. + +\textbf{KKT conditions (first-order).} + +$$ +\begin{aligned} +&\text{Stationarity:} && \grad f(x)-J_c(x)^{\!T}\lambda=0,\\ +&\text{Primal feasibility:} && c(x)\ge 0,\\ +&\text{Dual feasibility:} && \lambda\ge 0,\\ +&\text{Complementarity:} && \lambda^{\!T}c(x)=0\quad(\text{i.e., }\lambda_i c_i(x)=0\ \forall i). +\end{aligned} +$$ + +\textbf{Interpretation.} +\begin{itemize} +\item \emph{Active} constraints: $c_i(x)=0 \Rightarrow \lambda_i\ge 0$ can be nonzero (acts like an equality). +\item \emph{Inactive} constraints: $c_i(x)>0 \Rightarrow \lambda_i=0$ (no influence on optimality). +\end{itemize} +\end{frame} + + + + +\begin{frame}{Complementarity in plain English (and why Newton is tricky)} +\footnotesize + +\textbf{What $\lambda_i c_i(x)=0$ means.} +\begin{itemize} +\item Tight constraint ($c_i=0$) $\Rightarrow$ can press back ($\lambda_i\ge0$). +\item Loose constraint ($c_i>0$) $\Rightarrow$ no force ($\lambda_i=0$). +\end{itemize} + +\textbf{Why naive Newton fails.} +\begin{itemize} +\item Complementarity = nonsmooth + inequalities ($\lambda\ge0$, $c(x)\ge0$). +\item Equality-style Newton can violate nonnegativity or bounce across boundary. +\end{itemize} + +\textbf{Two main strategies (preview).} +\begin{itemize} +\item \emph{Active-set:} guess actives $\Rightarrow$ solve equality-constrained subproblem, update set. +\item \emph{Barrier/PDIP/ALM:} smooth or relax complementarity, damped Newton, drive relaxation $\to 0$. +\end{itemize} +\end{frame} + + + + \ No newline at end of file diff --git a/class02/ineq_constraints.tex b/class02/ineq_constraints.tex new file mode 100644 index 0000000..ae1f513 --- /dev/null +++ b/class02/ineq_constraints.tex @@ -0,0 +1,303 @@ +\section{Minimization w/ Inequality Constraints} + +\begin{frame}{Three families you should know (high level)} +\textbf{Goal:} Handle inequalities $c(x)\ge 0$ (and equalities) robustly and efficiently. + +\medskip +\textbf{Families.} +\begin{enumerate} +\item \textbf{Penalty}: embed violations in the objective; crank a parameter $\rho\uparrow$. +\item \textbf{Augmented Lagrangian (ALM)}: maintain multipliers \& a \emph{moderate} penalty; solve easier subproblems. +\item \textbf{Interior-Point (PDIP)}: enforce $c(x)>0$ via a barrier; follow the \emph{central path} with primal--dual Newton. +\end{enumerate} + +\textbf{Rule of thumb.} Penalty is simplest; ALM is a strong default for medium accuracy; PDIP is the gold standard for convex QPs and very robust with Newton. +\end{frame} + + + + +\begin{frame}{Inequality-Constrained Minimization} +\textbf{Problem Setup:} +$$ +\min f(x) \quad \text{s.t. } c(x) \geq 0 +$$ +\textbf{KKT conditions:} + +$$ +\nabla f - \left(\frac{\partial c(x)}{\partial x}\right)^T \lambda = 0 \quad \text{(stationarity)} +$$ + +$$ +c(x) \geq 0 \quad \text{(primal feasibility)} \quad \quad \quad \lambda \geq 0 \quad \text{(dual feasibility)} +$$ + +$$ +\lambda \circ c(x) = \lambda^T c(x) = 0 \quad \text{(complementarity)} +$$ + +\textbf{Unlike equality case, we can’t directly solve KKT conditions with Newton! Why?} + + +\end{frame} + + +\begin{frame}{Lots of solution methods to use: Active Set Method} +\underline{\textbf{Active Set Method}} +\begin{itemize} + \item High level idea: Guess which inequalities are redundant at optimality and throw them away. + \item Switch inequality constraints on/off in outer-loop and solve equality-constrained problem. + \item Works well if you can guess active set well ( common in MPC where good warm-starts are common). + \item Has really bad worst-time complexity. + \item Usually custom heuristics are used for specific problem classes/structure. + +\end{itemize} +\end{frame} + +\begin{frame}{Lots of solution methods to use: Penalty Methods} +\underline{\textbf{Penalty Method}}: Replace constraints with cost terms that penalize violation! +$$ +\min_x\; f(x) \;+\; \tfrac{\rho}{2}\,\big\|c^-(x)\big\|_2^2,\qquad +c^-(x):=\min(0,c(x))\ (\text{elementwise}). +$$ +\textbf{Algorithm sketch.} +\begin{enumerate} +\item Start with a small $\rho>0$; minimize the penalized unconstrained objective. +\item Increase $\rho$ (e.g., $\times 10$) and warm start from previous $x$. +\item Stop when $c^-(x)$ is small enough. +\end{enumerate} + +\textbf{Pros.} Dead simple; reuse unconstrained machinery (Grad/Newton + line search). \\ +\textbf{Cons.} Ill-conditioning as $\rho\to\infty$ to satisfy constraints.; struggles to reach high accuracy; multipliers are implicit. \\ +\textbf{Popular fix}: estimate $\lambda$ from penalty at each iteration to be able to converge with finite $\rho$. Called “Augmented Lagrangian” (also closely related to ADMM). +\end{frame} + + + + + + +% ---- ALM ---- +\begin{frame}{Augmented Lagrangian (ALM): fix penalty’s weaknesses} +\textbf{Core idea.} Introduce multipliers $\lambda$ so we can keep $\rho$ moderate and still achieve accuracy. + +\textbf{Lagrangian for equality case:} $\mathcal{L}_\rho(x,\lambda)=f(x)+\lambda^{\!T}C(x)+\tfrac{\rho}{2}\|C(x)\|_2^2.$ + +\textbf{Outer loop.} +\begin{enumerate} +\item $x^{k+1}\approx \arg\min_x \mathcal{L}_\rho(x,\lambda^k)$ (unconstrained solve). +\item $\lambda^{k+1}=\lambda^k+\rho\,C(x^{k+1})$. +\end{enumerate} + +\textbf{Inequalities (sketch).} Apply to the \emph{hinge} $c^-(x)$ and keep $\lambda\ge 0$: + +$$ +\mathcal{L}_\rho(x,\lambda)=f(x)-\lambda^{\!T}c(x)+\tfrac{\rho}{2}\|c^-(x)\|_2^2,\quad +\lambda^{k+1}=\max\!\big(0,\lambda^k-\rho\,c(x^{k+1})\big). +$$ + +\textbf{Why it works.} Subproblems are better conditioned than pure penalty; $\lambda$ estimates improve the model; finite $\rho$ can reach high accuracy. +\end{frame} + +\begin{frame}{ALM in practice (optimization loop view)} +\textbf{Inner solver.} Use (damped) Newton or quasi-Newton on $\mathcal{L}_\rho(\cdot,\lambda^k)$ with Armijo/Wolfe line search. \\ +\textbf{Tuning.} +\begin{itemize} +\item Keep $\rho$ fixed or adapt slowly (increase if feasibility stalls). +\item Scale constraints; monitor $|C(x)|$ and stationarity. +\end{itemize} +\textbf{When to pick ALM.} +\begin{itemize} +\item Nonconvex NLPs where feasibility progress matters and you want robust globalization. +\item Medium accuracy is fine, or as a precursor to a polished PDIP phase on a convex QP. +\end{itemize} + +\end{frame} + + + + + + + + + +\begin{frame}{Interior-Point / Barrier Methods} +Replace inequalities with barrier function in objective: + +$$ +\min f(x), \quad x \geq 0 \quad \to \quad \min f(x) - \rho \log(x) +$$ + +\begin{itemize} + \item Gold standard for convex problems. + \item Fast convergence with Newton and strong theoretical properties. + \item Used in IPOPT. +\end{itemize} + +(Diagram: $-\log(x)$ barrier.) + +\end{frame} + + + +\begin{frame}{Primal-Dual Interior Point Method} +$$ +\min f(x) \quad \text{s.t. } x \geq 0 +$$ + +$$ +\to \min f(x) - \rho \log(x) +$$ + +$$ +\frac{\partial f}{\partial x} - \frac{\rho}{x} = 0 +$$ + +\begin{itemize} + \item This “primal” FON condition blows up as $x \to 0$. + \item We can fix this with the “primal-dual trick.” +\end{itemize} +\end{frame} + + +\begin{frame}{The Primal-Dual Trick for IPM} +Introduce new variable $\lambda = \frac{\rho}{x} \quad \Rightarrow \quad x \lambda = \rho$. + +$$ +\begin{cases} +\nabla f - \lambda = 0 \\ +x \lambda = \rho +\end{cases} +$$ + + +\begin{itemize} + \item This can actually be viewed as a relaxed complementarity slackness from KKT! + \item Converges to exact KKT solution as $\rho \to 0$. + \item We lower $\rho$ gradually as solver converges (from $\rho \sim 1$ to $\rho \sim 10^{-6}$). + \item Note: we still need to enforce $x \geq 0$ and $\lambda \geq 0$ (with line search). +\end{itemize} +\textbf{We will use another approach from 2022 from a researcher at TRI that developped an even cooler trick.} + +\end{frame} + + +\begin{frame}{Log-Domain Interior-Point Method} +\textbf{More general constraint case}: \quad \quad \quad \quad \quad $\min f(x) \quad \text{s.t. } c(x) \geq 0$ + +\textbf{Simplify by introducing a “slack variable”:} + +$$ +\min_{x,s} f(x) \quad \text{s.t. } c(x) - s = 0, \; s \geq 0 +$$ + +$$ +\to \min_{x,s} f(x) - \rho \log(s) \quad \text{s.t. } c(x) - s = 0 +$$ + +\textbf{ Write out Lagrangian:} \quad \quad \quad $L(x,s,\lambda) = f(x) - \rho \log(s) - \lambda^T(c(x)-s)$ +\end{frame} + + +\begin{frame}{Log-Domain Interior-Point Method} +\textbf{Apply F.O.N.C to Lagrangian from last slide:} + +$$ +\nabla_x L = \nabla f - \left(\frac{\partial c}{\partial x}\right)^T \lambda = 0 +$$ + +$$ +\nabla_s L = \frac{\rho}{s} + \lambda = 0 \quad \Rightarrow \quad s \lambda = \rho +$$ + +$$ +\nabla_\lambda L = s - c(x) = 0 +$$ + +This second equation has a really nice interpretation: relaxed complementarity slackness + + +\end{frame} + +\begin{frame}{Log-Domain Interior-Point Method} +\textbf{To ensure $s \geq 0$ and $\lambda \geq 0$, introduce change of variables:} $$s = \sqrt{\rho} e^{\sigma}, \quad \lambda = \sqrt{\rho} e^{-\sigma}$$ + +Now (relaxed) complementarity is always satisfied by construction. + +Plug back into F.O.N.C + +$$ +\nabla f - \left(\frac{\partial c}{\partial x}\right)^T \lambda = 0 \quad \quad \quad c(x) - \sqrt{\rho} e^{\sigma} = 0 +$$ + +We can solve these with (Gauss) Newton: + +$$ +\begin{bmatrix} +H & \sqrt{\rho} c^T e^{-\sigma} \\ +c & -\sqrt{\rho} e^{\sigma} +\end{bmatrix} +\begin{bmatrix} +\delta x \\ \delta \sigma +\end{bmatrix} += +\begin{bmatrix} +-\nabla f + c^T \lambda \\ -c(x) + \sqrt{\rho} e^{\sigma} +\end{bmatrix} +$$ + + + +\end{frame} + + +\begin{frame}{Example: Quadratic Program} +Super common problem to be solved in control applications: quadratic programs +$$ +\min_x \tfrac{1}{2} x^T Q x + q^T x, \quad Q \succeq 0 +$$ + +s.t. + +$$ +Ax = b, \quad Cx \leq d +$$ + +\begin{itemize} + \item Super useful in control (SQP) + \item Can be solved very fast ($\sim kHz$). +\end{itemize} +\end{frame} + + + +\begin{frame}{Move to Julia Code} +\begin{center} + \textbf{Quick Demo of Julia Notebook: part3\_ipm.ipynb} +\end{center} +\end{frame} + + +% ---- Comparison ---- +\begin{frame}{Penalty vs.\ ALM vs.\ PDIP: what changes?} +\begin{itemize} +\item \textbf{Feasibility handling:} +\begin{itemize} +\item Penalty: encourages $c(x)\ge 0$ via cost; feasibility only in the limit $\rho\uparrow$. +\item ALM: balances optimality and feasibility via $\lambda$ updates at finite $\rho$. +\item PDIP: enforces strict interior $c(x)>0$; drives $s_i\lambda_i=\rho\to 0$. +\end{itemize} +\item \textbf{Conditioning:} +\begin{itemize} +\item Penalty gets ill-conditioned as $\rho$ grows. +\item ALM keeps conditioning reasonable. +\item PDIP maintains well-scaled Newton systems near the path (with proper scaling). +\end{itemize} +\item \textbf{Accuracy:} Penalty (low–med), ALM (high with finite $\rho$), PDIP (high; excellent for convex). +\item \textbf{Per-iteration work:} Penalty/ALM solve unconstrained-like subproblems; PDIP solves structured KKT systems with slacks/duals. +\end{itemize} + +\end{frame} + + \ No newline at end of file diff --git a/class02/intro.tex b/class02/intro.tex new file mode 100644 index 0000000..2313f3f --- /dev/null +++ b/class02/intro.tex @@ -0,0 +1,63 @@ + +% --- Slide 1: Title --- +\begin{frame}[plain] + \titlepage +\end{frame} +\section{Overview and Big Picture of Lecture 2} + +% ---- Learning goals ---- +\begin{frame}{Learning goals (what you’ll be able to do)} +\textbf{Goals for today} +\begin{itemize} +\item Pick and configure an optimizer for small control problems (unconstrained \& constrained). +\item Derive KKT conditions and form the SQP QP subproblem for a nonlinear program. +\item Explain the differences between penalty, augmented Lagrangian, and interior-point methods. +\end{itemize} +\textbf{Why?}\\ +In future classes, this will help us map classic control tasks (LQR/MPC/trajectory optimization) to QPs/NLPs and choose a solver strategy. +\end{frame} + +% ---- Agenda ---- +\begin{frame}{Roadmap for today (2\,hours)} +\begin{enumerate} +\item Big picture and some notation \hfill \textit{(5 min)} +\item Unconstrained optimization: Root-finding, Newton and globalization \hfill \textit{(30 min)} +\item Equality constraints: KKT, Newton vs. Gauss–Newton \hfill \textit{(20 min)} +\item Inequalities \& KKT: complementarity \hfill \textit{(10 min)} +\item Methods: penalty $\rightarrow$ ALM $\rightarrow$ interior-point (PDIP) \hfill \textit{(20 min)} +\item Brief look at SQP for solving hard control problems \hfill \textit{(20 min)} +\end{enumerate} +\end{frame} + + + +% ---- Big picture ---- +\begin{frame}[t]{Big picture: why optimization for control?} +\begin{columns}[T,onlytextwidth] + \column{0.54\textwidth} + \small + \begin{itemize}[<+->]\setlength{\itemsep}{2pt} + \item Controller synthesis often reduces to solving a sequence of optimization problems. + \item \textbf{MPC} solves a QP/NLP online at each time step; warm-start and sparsity are critical. + \item \textbf{Trajectory optimization} (nonlinear robots) uses NLP + collocation; needs robust globalization. + \item \textbf{Learning-based control} backpropagates through optimizers (differentiable programming). + \end{itemize} + + \column{0.42\textwidth} + \centering + \resizebox{\columnwidth}{!}{% + \begin{tikzpicture}[ + node distance=10mm and 12mm, + every node/.style={font=\small}, + shorten >=2pt, + shorten <=2pt + ] + \node[box] (plant) {Dynamics\\$x_{k+1}=f(x_k,u_k)$}; + \node[box, below=of plant] (opt) {Online optimizer\\(QP/NLP)}; + + \draw[->] (opt.north) -- node[pos=0.55, right=2pt] {$u_k$} (plant.south); + \draw[->] (plant.east) -- ++(0.6,0) |- node[pos=0.25, right=2pt] {$x_k$} (opt.east); + \end{tikzpicture}% + } +\end{columns} +\end{frame} diff --git a/class02/main.tex b/class02/main.tex new file mode 100644 index 0000000..07d55bf --- /dev/null +++ b/class02/main.tex @@ -0,0 +1,82 @@ +\documentclass[aspectratio=169,11pt]{beamer} + +% --- Theme (portable by default; auto-use metropolis if available) --- +\newif\ifusemetropolis +\IfFileExists{beamerthememetropolis.sty}{\usemetropolistrue}{\usemetropolisfalse} +\ifusemetropolis + \usetheme[numbering=fraction]{metropolis} % nice minimal look with x/y counter + \metroset{block=fill,progressbar=foot,sectionpage=progressbar} +\else + \usetheme{Boadilla} + \usecolortheme{seahorse} + \setbeamertemplate{footline}[frame number] % x/y in the footer +\fi +\setbeamertemplate{navigation symbols}{} % hide nav icons + +% --- Packages you’ll likely want for math/notation --- +\usepackage{amsmath,amssymb,mathtools} +\usepackage{bm} +\usepackage{graphicx} +\usepackage{booktabs} % tables later if needed +\usepackage{microtype} % nicer text (pdflatex) +\usetikzlibrary{positioning,arrows.meta} + +% --- Handy macros for optimization/control --- +\DeclareMathOperator*{\argmin}{arg\,min} +\DeclareMathOperator*{\argmax}{arg\,max} +\newcommand{\R}{\mathbb{R}} +\newcommand{\E}{\mathbb{E}} +\newcommand{\ip}[2]{\left\langle #1,\, #2 \right\rangle} +\newcommand{\norm}[1]{\left\lVert #1 \right\rVert} +\providecommand{\grad}{\nabla} +\providecommand{\hess}{\nabla^2} +\newcommand{\Lag}{\mathcal{L}} + +% --- Auto section title frames (useful as your deck grows) --- +\AtBeginSection{ + \begin{frame}[plain] + \vfill + \centering + {\usebeamerfont{title}\insertsection} + \vfill + \end{frame} +} + +\usetikzlibrary{positioning,arrows.meta} +\tikzset{ + >=Stealth, + box/.style={ + draw, + rounded corners, + align=center, + inner sep=4pt, + minimum width=3.2cm, + minimum height=1.1cm + } +} + + +% Use outer theme that shows dots for sections +%\useoutertheme{miniframes} + + + + +% --- Title info (update these) --- +\title{Lecture 2: Numerical Optimization for Control\\\small(grad/SQP/QP; ALM vs. interior-point vs. penalty)} +\author{Arnaud Deza} +\institute{ISYE 8803: Special Topics on Optimal Control and Learning} +\date{\today} + + + + +\begin{document} +\include{intro} +\include{notation} +\include{root_finding} +\include{eq_constraints} +\include{ineq_constraints} +\include{SQP} + +\end{document} \ No newline at end of file diff --git a/class02/notation.tex b/class02/notation.tex new file mode 100644 index 0000000..d38fcd9 --- /dev/null +++ b/class02/notation.tex @@ -0,0 +1,33 @@ +\begin{frame}{Some Notation:} +Given $f(x): \mathbb{R}^n \to \mathbb{R}$ \quad \quad \quad \quad \quad \quad \quad \quad $\frac{\partial f}{\partial x} \in \mathbb{R}^{1 \times n} \quad \text{is a row vector}$ + +This is because $\frac{\partial f}{\partial x}$ is the linear operator mapping $\Delta x$ into $\Delta f$: + +$$ +f(x + \Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x +$$ + +Similarly $g(y): \mathbb{R}^m \to \mathbb{R}^n$ \quad \quad \quad \quad \quad $\frac{\partial g}{\partial y} \in \mathbb{R}^{n \times m} \quad \text{because}$ + +$$ +g(y+\Delta y) \approx g(y) + \frac{\partial g}{\partial y}\Delta y +$$ +\end{frame} + +\begin{frame}{Some notation:} +For convenience, we will define: + +$$ +\nabla f(x) = \left(\frac{\partial f}{\partial x}\right)^T \in \mathbb{R}^n \quad \text{(column vector)} +$$ + +$$ +\nabla^2 f(x) = \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial x}\right) = \frac{\partial^2 f}{\partial x^2} \in \mathbb{R}^{n \times n} +$$ + +$$ +f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x + \tfrac{1}{2}\Delta x^T \nabla^2 f(x)\Delta x +$$ + +\end{frame} + diff --git a/class02/root_finding.tex b/class02/root_finding.tex new file mode 100644 index 0000000..ae47f23 --- /dev/null +++ b/class02/root_finding.tex @@ -0,0 +1,156 @@ + +\section{Root-Finding} + +\begin{frame}{Root Finding} +Given $f(x)$, find $x^*$ such that $f(x^*) = 0$ (example: finding equilibrium of a continuous-time dynamics). + +Closely related: fixed point \quad \quad \quad $f(x^*) = x^* \quad (\text{equilibrium of discrete-time dynamics})$ + +\textbf{Fixed-Point Iteration} +\begin{itemize} + \item Simplest solution method + \item If fixed point is stable, just “iterate the dynamics” until it converges + \item Only works if $x^*$ is a stable equilibrium point and if initial guess is in the basin of attraction + \item can converge slowly (depends on $f$ i.e depending on eigenvalues) +\end{itemize} +Gradient Descent in Fixed Point Iteration applied to gradient of function $f$. +\end{frame} + + + +\begin{frame}{Newton's Method} +TLDR: Instead os solving for $f(x) =0$, solve a linear for a linear approximation of $f(x)$.\\ +Fit a linear approximation to $f(x)$:\quad $f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x$ + +Set approximation to zero and solve for $\Delta x$: + +$$ +f(x) + \frac{\partial f}{\partial x}\Delta x = 0 \quad \Rightarrow \quad \Delta x = -\left(\frac{\partial f}{\partial x}\right)^{-1} f(x) +$$ + +Apply correction: $x \leftarrow x + \Delta x$ +Do this in a loop and repeat until convergence. + +\end{frame} + +\begin{frame}{Example: Backward Euler} +Last time: Implicit dynamics model (nonlinear function of current state and future state) +$$ +f(x_{n+1}, x_n, u_n) = 0 +$$ +Implicit Euler: this time we have $x_{n+1}$ on the right; i.e evaluate f at future time. +$$ +x_{n+1} = x_n + h f(x_{n+1}) +$$ + +(Evaluate $f$ at future time) + +$$ +\Rightarrow f(x_{n+1}, x_n, u_n) = x_{n+1} - x_n - h f(x_{n+1}) = 0 +$$ +Solve root finding problem for $x_{n+1}$ +\begin{itemize} + \item Very fast convergence with Newton (quadratic) and can get machine precision. + \item Most expensive part is solving a linear system $O(n^3)$ + \item Can improve complexity by taking advantage of problem structure/sparsity. +\end{itemize} +\end{frame} + + +\begin{frame}{Move to Julia Code} +\begin{center} + \textbf{Quick Demo of Julia Notebook: part1\_root\_finding.ipynb} +\end{center} +\end{frame} + + +\begin{frame}{Minimization} +$$ +\min_x f(x), \quad f(x): \mathbb{R}^n \to \mathbb{R} +$$ +If $f$ is smooth, $\frac{\partial f}{\partial x}(x^*) = 0$ at a local minimum. + +Hence, now we have a root-finding problem $\nabla f(x) = 0$ $\Rightarrow$ Apply Newton! + +$$ +\nabla f(x+\Delta x) \approx \nabla f(x) + \frac{\partial}{\partial x}(\nabla f(x))\Delta x = 0 +\quad \quad \quad \quad +\Rightarrow \Delta x = -(\nabla^2 f(x))^{-1}\nabla f(x) +$$ + +$$ +x \leftarrow x + \Delta x +$$ + +Repeat this step until convergence; Intuition to have about Newton: +\begin{itemize} + \item Fitting a quadratic approximation to $f(x)$; Exactly minimize approximation +\end{itemize} + +\end{frame} + + +\begin{frame}{Move to Julia Code} +\begin{center} + \textbf{Quick Demo of Julia Notebook: part1\_minimization.ipynb} +\end{center} +\end{frame} + + + +\begin{frame}{Take-away Messages on Newton} +Newton is a local root-finding method. Will converge to the closest fixed point to the initial guess (min, max, saddle). + +\textbf{Sufficient Conditions} +\begin{itemize} + \item $\nabla f = 0$: “first-order necessary condition” for a minimum. Not a sufficient condition. + \item Let’s look at scalar case: $\Delta x = -\frac{1}{\nabla^2 f}\nabla f$ +\end{itemize} +where: negative corresponds to “descent”, $\nabla f$ corresponds to the gradient and $\nabla^2 f$ acts as the “leading rate” / “step size”. + +$\nabla^2 f > 0 \quad \Rightarrow \quad \text{descent (minimization)} \quad \quad \quad \nabla^2 f < 0 \quad \Rightarrow \quad \text{ascent (maximization)}$ +\begin{itemize} + \item In $\mathbb{R}^n$, if $\nabla^2 f \succeq 0$ (positive definite) $\Rightarrow$ descent + \item If $\nabla^2 f > 0$ everywhere $\Rightarrow f(x)$ is strongly convex → Can always solve with Newton + \item Usually not the case for hard/nonlinear problems +\end{itemize} + \end{frame} + +\begin{frame}{Regularization: Ensuring Local Minimization} +Practical solution to make sure we always minimize: + +If $H$ ($H \leftarrow \nabla^2 f$) not positive definite, we just make it so with regularization. + + +While $H \not\succeq 0$: +$$H \leftarrow H + \beta I \quad (\beta > 0 \ \text{scalar hyperparameter})$$ + +Then do newton step as usual. I.e: + +$$ +x \quad \leftarrow \quad x + \Delta x \quad = \quad x -H^{-1}\nabla f +$$ + +\begin{itemize} + \item also called “damped Newton” (shrinks steps) + \item Guarantees descent + \item Regularization makes sure we minimize, but what about over-shooting? +\end{itemize} +\end{frame} + +\begin{frame}{Line Search: Mitigating overshooting in Newton} +\begin{itemize} + \item Often $\Delta x$ step from Newton overshoots the minimum. + \item To fix this, check $f(x + \alpha \Delta x)$ and “back track” until we get a “good” reduction. + \item Many strategies: all differ in definition of good. + \item A simple + effective one is \textbf{Armijo Rule}: +\end{itemize} + +Start with $\alpha=1$ as our step length and have tolerance $b$ as a hyper-parameter. + $$ +\text{while } f(x + \alpha \Delta x) > f(x) + b \alpha \nabla f(x)^T \Delta x: \quad \quad \alpha \leftarrow c \alpha \quad (\text{scalar } < 1 \text{ i.e } c =\frac{1}{2}) +$$ +\footnotesize +The intuition behind this is that $\alpha \nabla f(x)^T \Delta x$ corresponds to the expected change in $f$ based on a 1st order taylor series expansion. I.e we are checking the actual decrease in $f$ agrees with a $1st$ order taylor approximation within a tolerance $b$. + +\end{frame} \ No newline at end of file From 4bcd7640907b28fe4b6697e34dd782b608326c4c Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Fri, 29 Aug 2025 09:08:42 -0400 Subject: [PATCH 2/8] Add missing Lecture 2 notebooks --- class02/part1_minimization.ipynb | 721 +++++++++++++++++++++++++++++ class02/part1_root_finding.ipynb | 442 ++++++++++++++++++ class02/part2_eq_constraints.ipynb | 398 ++++++++++++++++ class02/part3_ipm.ipynb | 639 +++++++++++++++++++++++++ 4 files changed, 2200 insertions(+) create mode 100644 class02/part1_minimization.ipynb create mode 100644 class02/part1_root_finding.ipynb create mode 100644 class02/part2_eq_constraints.ipynb create mode 100644 class02/part3_ipm.ipynb diff --git a/class02/part1_minimization.ipynb b/class02/part1_minimization.ipynb new file mode 100644 index 0000000..c1cf0aa --- /dev/null +++ b/class02/part1_minimization.ipynb @@ -0,0 +1,721 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e5af1721", + "metadata": {}, + "source": [ + "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()" + ] + }, + { + "cell_type": "markdown", + "id": "62dc7858", + "metadata": {}, + "source": [ + "# Lecture 3 — Minimization via Newton's Method \n", + "## Key ideas:\n", + "### • ∂f/∂x is a row vector; we use ∇f(x) = (∂f/∂x)^T (column)\n", + "### • Newton for minimization solves: H(x) Δx = -∇f(x)\n", + "### • Update: x ← x + Δx, where H = ∇²f is the Hessian\n", + "### • If H ≻ 0 (positive definite), the Newton step is a descent direction\n", + "### • Regularization (\"damped Newton\"): add βI until H ≽ 0 to guarantee descent \n", + "### • Line Search: avoid overshooting a minima" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "c53d0314", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using ForwardDiff\n", + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "fa9ed072", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "f (generic function with 1 method)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "f(x)\n", + "\n", + "\n", + "Scalar objective used to illustrate Newton's method on a nonconvex quartic.\n", + " \n", + "\n", + "f(x) = x^4 + x^3 - x^2 - x\n", + "\n", + "\n", + "This function has both minima and maxima, so a naive Newton step can ascend if\n", + "`∇²f(x) < 0` at the current iterate (see lecture notes on sufficient conditions).\n", + "\"\"\"\n", + "\n", + "function f(x)\n", + " return x.^4 + x.^3 - x.^2 - x\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "9d7ccc4e", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "∇f" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "∇f(x)\n", + "\n", + "Analytic gradient (first derivative) of `f`.\n", + "\"\"\"\n", + "function ∇f(x)\n", + " return 4.0*x.^3 + 3.0*x.^2 - 2.0*x - 1.0\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a666f177", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "∇2f (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "Analytic Hessian (second derivative) of `f`.\n", + "\"\"\"\n", + "\n", + "function ∇2f(x)\n", + " return 12.0*x.^2 + 6.0*x - 2.0\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6ca76dc3", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1000-element LinRange{Float64, Int64}:\n", + " -1.75, -1.747, -1.74399, -1.74099, …, 1.24099, 1.24399, 1.247, 1.25" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = LinRange(-1.75,1.25,1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "39faff1e", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p = plot(x,f(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "77ce22be", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "newton_step (generic function with 1 method)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function newton_step(x0)\n", + " xn = x0 - ∇2f(x0)\\∇f(x0)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "6d55bff0", + "metadata": {}, + "source": [ + "### Let's check that our newton step implementation is doing what we expect should happen in a \"nice region\" of the function (think basin of attractions)." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "193f1b88", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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2IKG27oWeFwCAM8o4UyrlVTZd5mD0TCOn63k5lx07dujhJCvrXxdeDuWVyOmSSqObAwDAOYt1kyICDd8awOE9L8XFxZKWltbw+MiRIzqMhIWFSfv27fWQT2Zmprz33nv66y+//LIkJiZKjx49pLy8XN5++21ZuXKlfP3112JlbQK8pXNkoBzMLdZDR1d0jzK6SQAA/LRY1wmGjBweXrZs2SJjxoxpePzoo4/q29tuu03mz5+v13BJT09v+HplZaU89thjOtD4+/tLr1695Jtvvmn037CqAR3a6PCy5ehpwgsAwKkccKJiXYeHFzVTSK1dcj4qwJzt8ccf14crGpAQJh9/n0HdCwDA6aRm14aXbjHOEV6cvubFVaieF2VXZgGbNAIAnEZlta1hplFydLA4A8KLk2gf5i8RQT5SVWOXncfZpBEA4BwO5RXrDYSDfD2lXYivOAPCi5NQ2wKcvVUAAADONGTUNTrIabawIbw4kf4JtYvVsUkjAMBZ7Muu3Xanq5MMGSmEFyfS0PNy9LRezRAAAKfpeYlxjmJdhfDiRLrHBIu/t4cUlldLat20NAAAjLQ/6z/DRs6C8OJEPD3cG/Y52nj4lNHNAQC4uPzSSskuLNf3uzjJGi8K4cXJDOlIeAEAOIf9dUNGcW38JMjXS5wF4cXJDOnYVt9uOkLdCwDAWPuznK9YVyG8OJmesSG67iW/tIq6FwCAoVJznGtl3XqEFyfjRd0LAMBJ7Ksr1k12omJdhfDihKh7AQAYzWazN2zIyLARfhZ1LwAAo2WcKZXSyhrx9nSXDm39xZkQXpy87qW+0hsAACOGjLpEBeqlPJyJc7UGGnUvAABnWVk3Ocq5howUwouTGlo3dER4AQAYYX/dnkbONtNIIbw4edEudS8AAGN3kw4WZ0N4cVIpsSES4O0hBWXUvQAAWldZZY0cOVXilNOkFcKLk6LuBQBglAM5RWK3i7QN8JaIIB9xNoQXE0yZXn+I8AIAaD1767YF6N7O+YaMFMKLExvWqW69l8OnpLrGZnRzAAAuYs+JAn1LeMFF1b2E+HlJUUW1/HA83+jmAABcxJ4TtT0vPdqFiDMivDgxD3c3GZ5U2/uy9iBDRwAAx6ux2WV/3QJ13WPoecFFGJEUoW/XpuUZ3RQAgAs4crJEyqpqxM/LQxLDA8QZEV6c3GWdw/Xt9vR8Ka6oNro5AAAXqXfpFhOkRwCcEeHFycWH+Uv7MH+pttl14S4AAI6018nrXRTCiwmMqOt9+e7gSaObAgBwkWLd7k4600ghvJjAZUm14WVtGuEFAOA4dru9YdioB+EFl2JYp3BRw45pucWSXVBudHMAABaVXVguZ0qrdK1Llyjn2xagHuHFBEL8vaRnXKi+T+8LAMBR9mTWDhl1jgwUXy8PcVaEF5MY0bDeC1OmAQCuW++iEF5Mt97LSbHZ7EY3BwBg5W0BYggvaAH9E9pIoI+nnCyulN11by4AAFxpW4B6hBeT8PZ0lxF1s45WpzJ0BABoWQWlVZKZX6bvM2yEFjM6uXboaFVqrtFNAQBYzJ6s2l79+DA/vSmwMyO8mMjo5Eh9uyMjX06XVBrdHACAFVfWjXHuISOF8GIi0SG+0jU6SOx2tdouQ0cAANebaaQQXkxmTNfa3pdV+xk6AgC0HDOsrFuP8GIyo7vU1r2sOXhSapgyDQBoAaWV1XoVdyUllmEjtLB+CW0kyNdT17zsPJ5vdHMAABapd7HZRaKCfSQq2FdcOrysWbNGJk6cKO3atRM3NzdZtGjRz75m9erV0q9fP/Hx8ZGkpCSZP3++I5toOl4e7nJZ3S7TTJkGALSEncdrh4x6xtZuRePS4aWkpER69+4tc+bMadLzjxw5IhMmTJAxY8bIjh075OGHH5a77rpLli1b5shmmnbW0WqmTAMAWsCuzNrw0ivO+YeMFE9H/sevvvpqfTTV3LlzJTExUV588UX9uFu3brJ27Vp56aWXZNy4cQ5sqTnrXnZmFkhuUblEBjl/Fx8AwHn9UFeG0NMk4cWpal42bNggY8eObXROhRZ1/nwqKiqksLCw0WF1kcG+0jsuRE+ZXrmP3hcAwMUrKq+Sw3kl+n4vExTrOl14yc7OlqioqEbn1GMVSMrKapcs/rFZs2ZJSEhIwxEfHy+uYGy32uu0fG+O0U0BAJjY7szaP/pjQ/2kbaCPmIFThZeLMX36dCkoKGg4MjIyxBVc0SOqYZdpNcUNAICLsSsz31T1Lg6veWmu6Ohoyclp3JOgHgcHB4ufn985X6NmJanDpTz7rCS7u0t82AjJOF0maw6clKtSomu/9txzIjU1+jkAADR5ppGJwotT9bwMHTpUVqxY0ejc8uXL9XmcxcND3J55Rmb+sFA//GZfzn+Cy4wZ+usAADRrppFJpkk7vOeluLhY0tLSGk2FVlOgw8LCpH379nrIJzMzU9577z399XvvvVdmz54tjz/+uNxxxx2ycuVK+eyzz+SLL75wZDPN5+mn9c2YGTPkwRFn5MOA28Q2c6a4P/OMyMyZDV8HAOBCCkqr5NipUn2/p0mKdR0eXrZs2aLXbKn36KOP6tvbbrtNLz6XlZUl6enpDV9X06RVUHnkkUfklVdekbi4OHn77beZJn0uTz+ttwd47NlnZNqGT8W9pprgAgC4qF6XhLb+EuLvJWbhZrerCbfWoWYmqVlHqnhX1cpYXbWXt3hWV0m1p5d4VlUa3RwAgIm8vjpNnl+aKtf0ipHZN/czzee3U9W8oJmee04HlwoPT31rVz0vAAA00a66Yl0zzTRyutlGaIa64tyKGc9Kz+pBcs+aD+UxVfPi5sbQEQDAknsa1SO8mFH9rKKZM8Xn6adlxPzN8lrNTTKsU7gMVecVAgwA4ALyiiokM79M/82bEmuuMguGjcxIreNyVnHu+J4x+vbZ3tfXnldfBwDgAnZk1C5O1zkyUIJ8zVOsq9DzYkY/WoDuim5R4uXhJqk5RZL26COSFBloWNMAAOawI+OMvu0Tb64hI4WeFwtQ09uGJ4Xr+1/tyjK6OQAAE9ieXtvz0rd9GzEbwotF1A8dfUF4AQD8DLVOWH2xLj0vMMyV3aPE091N9mcXyeG8YqObAwBwYmm5xVJcUS3+3h7SJSpIzIbwYhGh/t4yrH7oaHe20c0BAJig3qVXXIh4uLuJ2RBeLGRCz9qdpb/YydARAMCa9S4K4cVCrugerRP03qxCOXqyxOjmAACcfJp0HxPWuyiEFwsJC/CWYZ3a6vv//uGE0c0BADih4opqvbSG0pfwAmdwbe92+nbRjkyx2J6bAIAWsPN4vqiPh9hQP4kM9hUzIrxYzFUp0eLj6S6H8kpkz4lCo5sDAHDSepc+7c3Z66IQXixGLfE8tluUvr9oe6bRzQEAOGm9S1+TDhkphBcLuq5vrL791w8n9EJEAAAoqpzgPzONCC9wIqO6REiov5fkFlXIxsOnjG4OAMBJHD9TJieLK/R+eD3ahYhZEV4syNvTvWG7AIaOAAD1tqXXLk7XPSZYfL08xKwILxZ1XZ/YhtV2y6tqjG4OAMAJbD56Wt8O6BAmZkZ4sagBCW30NDg1n3/FvlyjmwMAcAJbjp5p+IwwM8KLRbm7u8mkPrVrvvxja4bRzQEAGKywvKphcbr+HQgvcFK/GRCvb789kCfZBeVGNwcAYKDt6bWL07UP85fIIHMuTleP8GJhieEBMqhDmKjZ0v/cdtzo5gAADLSlod7F3L0uCuHF4n4zIE7ffr4lg+0CAMCFbWmodzF3sa5CeLG4Cb1iJMDbQ46eKpXvj9SmbgCAa6mqsTWsrEvPC5yev7enTKzbrPGzLQwdAYAr2pdVKGVVNRLs6ylJEYFidoQXFyrc/XJXlhSVVxndHABAK9tcN2TUP6GNno1qdoQXF9Cvfah0igjQqfvfP2QZ3RwAQCvbeswai9PVI7y4ADc3N7lhYG3vyyeb041uDgCgFdntdsssTleP8OIift0/Xu95tPN4QUPRFgDANTZjzC2q3Yyxd7x5d5I+G+HFRYQFeMs1dZs1vr/hmNHNAQC0ku/rZpqqXaTNvBnj2QgvLuTWoQn69t87T8jpkkqjmwMAaAWbjpzSt4M7WqPeRSG8uJA+8aGSEhssldU2vWgdAMD6NtX1vAxJbCtWQXhxscLdyUM66PsfbDomNrVvAADAsrIKyuTYqVJRs6OtsDhdPcKLi1EL1qlFijJOl+kNGwEA1rXpcG2vS0psiAT5eolVEF5cjJ+3R8Oide9uOGp0cwAArVHvkmideheF8OKCbh2SIG5uIqtT8yQtt8jo5gAAHGRjXc/LYAvVuyiEFxfUITxArugWpe+//d0Ro5sDAHCAnMJyOXKyRP+xOpCeF1jB3SM76tsF2zMlr6jC6OYAAFrYxsO1Q0bdY4IlxM869S6tFl7mzJkjHTp0EF9fXxk8eLB8//33533u/Pnz9ayYsw/1OrQstTmXmjqtpk2/T+0LAFh3inRHaw0ZtUp4+fTTT+XRRx+VZ555RrZt2ya9e/eWcePGSW5u7nlfExwcLFlZWQ3HsWOsCNvSVCis7315f+MxKausMbpJAIAWtOmwNYt1WyW8/O1vf5OpU6fKlClTpHv37jJ37lzx9/eXefPmXfCDNTo6uuGIiqqtz0DLGtcjWuLD/ORMaZX8Y9txo5sDAGghuUXlciivtt5lEOGleSorK2Xr1q0yduzY/3xDd3f9eMOGDed9XXFxsSQkJEh8fLxMmjRJ9uzZc97nVlRUSGFhYaMDTePh7iZ3Dk/U9//vu8NSw6J1AGCp/Yy6RgdLqL+3WI1Dw8vJkyelpqbmJz0n6nF2dvY5X5OcnKx7ZRYvXiwffPCB2Gw2GTZsmBw/fu6egVmzZklISEjDoQIPmk6t+RLq7yVHT5XKkp0njG4OAKAFrD9k3SEjp5xtNHToUJk8ebL06dNHRo0aJQsWLJCIiAh58803z/n86dOnS0FBQcORkcGePc0R4OMpd42o7X15bWUaWwYAgAWsSzupb0ckhYsVOTS8hIeHi4eHh+Tk5DQ6rx6rWpam8PLykr59+0paWto5v+7j46MLfM8+0DyTh3XQWwak5RbLV7vP3SMGADCHjNOlej8jVRpgpZ2kWy28eHt7S//+/WXFihUN59QwkHqseliaQg077dq1S2JiYhzYUtcW7OsldzT0vhyk9wUATGz9odpeF7UchpX2M2rVYSM1Tfqtt96Sd999V/bt2yf33XeflJSU6NlHihoiUkM/9WbOnClff/21HD58WE+tvuWWW/RU6bvuusvRTXVpU4YlSpCPp+zPLpKv9zbuKQMAmMfatNp6l+EWHTJSPB39DW644QbJy8uTGTNm6CJdVcuydOnShiLe9PR0PQOp3pkzZ/TUavXcNm3a6J6b9evX62nWcJwQfy+5bVgHmb0qTV5dcVDG9YjSU9YBAOZhs9llvcXrXRQ3u91uqTECNVVazTpSxbvUvzTPmZJKGfG/K6Wkskbe+F0/ubonQ3UAYCZ7TxTK+Fe/E39vD9kx40rx9nS6eTkt8vltnp8KDtcmwFvuvKx21d0XlqVKdY3N6CYBAC5iltHgxDBTBZfmsu5Phosy9bJEaRvgLYdPlshnW1h1FwDMZG1deLFyvYtCeEEjqjJ92i+S9P2XvznAnkcAYBIV1TUNK+uO6Ex4gYu5eXB7vedRblGFzFt3xOjmAACaYHt6vpRV1Uh4oLckRwWJlRFe8BM+nh7y2BXJ+v7cbw/pQl4AgDnqXYZ1Crf8bFHCC87p2t7tpHtMsBSVV8uLy1ONbg4A4Gd8eyDP8lOk6xFecE7u7m4yY2Lt2jofbUqXPScKjG4SAOA8ThZXyM7jtb+nRyVHiNURXnBeQzq2lYm924naLeDZf+0Riy0JBACWsaau16VbTLBEBfuK1RFecEFPju8qfl4esvnoGVm844TRzQEAnMPq1NrwMtoFel0UwgsuKCbEr2Hq9P98uU+KK6qNbhIA4Cw1NrusOVgbXsYkR4orILzgZ911WaIktPXXU6df/JriXQBwJjuP50t+aZUE+XpKv/ah4goIL2jS1OmZk1L0/fnrj8q29DNGNwkA8KMho8s6h4unh2t8rLvGT4lLNqpLhFzfL1ZUze7j/9ipV3IEABhvdV2x7ugurjFkpBBe0GRPT+iuV25Myy2WOSvTjG4OALi8U3qKdL7LTJGuR3hBs3ad/vO1tcNHr68+JPuyCo1uEgC4tO8OntQ94q4yRboe4QXNMr5ntIzrESXVNrs88ukOKa9i+AgAjLI6NdelpkjXI7ygWdR+Gc9dlyJtA7xlf3aRPL+U2UcAYITqGttZ9S6EF+CCIoN85flf99L31a7T9ckfANB6thw7o6dIt/H3kv4JbcSVEF5wUS7vFiWThybo+3/4fKfkFVUY3SQAcCnf7M3Rt2O6RrrMFOl6rvXTokU9Ob6bdIkK1BuCPfjxNt2FCQBwPLvdLsv31YaXK7tHiashvOCi+Xp5yOu/6ycB3h6y8fBpeX4Z9S8A0BoO5hbLsVOl4u3pLpd1dq16F4XwgkuSFBkkL/ymt77/9zWH5ctdWUY3CQAsb3ndkNHwTm0lwMdTXI3r/cRoceN7xsg9IzvKm2sOyx8+/0Hah/lLSmyI0c2CA6khwrziCsktrJCCsiopKq+W4oraWzV93mav3SxOdW3b9RYT7uLn7Sn+3h76CPb1koggH32omWuuNl4PtFR4uaJ7tLgiwgtaxB/HJcverEK9YNId8zfLogeGS7tQP6ObhUtQUFolh04Wy+G8EjmUVyxHT5bIiYJyyS4o0wXaKqC0BDc3kbYBPtI+zE86RgRKYniAdAwPkM5R6n6geLi7tcw3Aiwit7BcdmTUrqp7eTfX2RLgbIQXtAj1l/Oc3/WTX7+xXg7kFOsA8/m9QyXI18vopuFnqN6RrIJy2ZVZILszC+puC3Uh9oV4urvpnpMQPy/dkxLo66l3tfX19BB3dzdRnSnuKpmISEWVTUqraqSsslpKK2v09E7Vc6OWNlchSH0vdWxLr/2FXE/VU/WIDZHecSHSMy5UBnUIk+gQ11lFFDiXFftrl6foHR/qUqvqno3wghajPsDm3T5Qfvn6er2A3T3vb9WPVWEvnGvIZ8+JQvn+yGnZdOS0bE8/I6dKKs/53OhgX+kYESCd6npEYtv4SUyIrz7fNtDnkntF1NDSqZLa4aejp0p0L8+Rk+q2WIfgksoa3U511FPtGd4pXIZ1aitDO7WVUH/vS2oDYNoho26u2euiuNnVn10WUlhYKCEhIVJQUCDBwcFGN8clqU3Cbvr7Rv3Bc3nXSHnjlv66Ih7GUAFB/X+yLu2kDivbjp3R/9+cTYWQzpGB0kv1cMSG6JqlzlFBEmhgIaAKWYfySnTbVW/Q9vR82XOioNFwlWr3wA5tZFyPaLmyR7TEMlQJiyuuqJZ+zy2XymqbLHt4pCRHB4krfn4TXuAQGw+fktvmfS8V1TaZ0DNGXrmxD0WZrUjVpHx3ME9Wp+bp2zOlVY2+HuzrKYMSw/QxoEOYdI8JNkUPmarD2XjklKxPOynrDp3SO5yfTQWvib1j5Lo+sRLpot3psLbFOzLloU926LqwFY+N0lu2WAXhhfDiFNS2AVPf2yJVNXa9oePLN/SlB8ZB1D9jVaeybE+2rD6Qq++fLcjHU4YnhethFhVYkqOCdF2K2aWfKpWv92brn1stlV7/20z9aCO7RMj1/eL0Al5mCGZAU9z93hb5em+OTBuTJH8YlyxWQnghvDiNr/dkywMfbdMBZlSXCJl7S3/x8+aDpCWof7pqxsFXu7P1+jrHz5Q1+nqPdsF6p9lRXSKlb/tQ8bJ4z5fqbVIhZsG2440Kf1Uv028HxMvkoR2kfVt/Q9sItNSQ0Ze/v0y6t7PWZxzhhfDiVNYcyNPFu2VVNTIgoY28NXmAtAmgyPJi2Gx22ZZ+Rr7clS1Ld2fpqcv1fL3cZUxypN53amSXcL2BpqtSRb8qxCzYlimZ+bWhTvWuq+tz27AOcllSuCV6nuCaQ0aJ4QGy0mJDRgrhhfDidLYeOy23v7NZL2KW0NZf/u+2gZIUGWh0s0xTcLv56Gn5aleW7mXJPWsTTLXgmwor41OiZVRyhPh7M4Hwx2FPDaO9u/6YfHsgr+G82pPr/tFJck2vGGqxYBr3vL9Flu3JkQfGdJI/jusqVkN4Ibw4pdTsIrnz3c16eEOtB/LaTX1ldLLrTvX7uZk2amaQGg5SQyEniysb1a+M7R4lV6dE67oO6jmaRk2/fn/jMfl8y3Hd/a6o1aDvHdVJftU/Vnw8uY5wXiV1Q0ZqEsQXvx8hPdpZbxVzwgvhxWmpRcnu/WCrbD56Rnfj3zeqkzx6RRf++hWRqhqbrD90SvewqMBy9gwhVbehpgKrwmdVeMsH7cVT2xl8sPGY/N/aI3K6bn2bqGAf+f3lnXVtjNVrg2BO//rhhPz+4+3Soa2/rPrDaMsNGSmEF8KLU6uorpGZ/94rH25K14/7J7SRl2/oI/Fh/i55LdT6K6qGRS08pT5Y67Xx99Lrl1zdM0aGdmzLTK0WVlZZI59sTtcbiqoVhhX1wfDolclyTc8YamLgVO59f6ss3ZMt94/uJI9fZb0hI4XwQngxhS92ZskT/9wpRRXV4uflofdHUsWUVt/LRn1oqvoLVXC7Yl+u/vnrhQd668CiNrscnBhGj1QrBciPN6XL7FVpDcNzat2bx69KZlgTTjNk1P+/lkt5lU2WPDjCshvfEl4IL6Zap+OP//hB13cofeJD5dlre+hbKyksr5JV+3Nl6e5svXCcmnlVLzLIR9evqB6WgR3CLB/enPkDYt7aI3p39PqaGDXV/OlruuvtEQCjLNx+XB759AfLzjKqR3ghvJhuRsjHm9Nl1pf7Gz40JvVpp3ti4tqYdyhJbTS4Yl+OniGkhobUWjf11DL2V6VE66N/+zYMUTgRVQfz+qo0eXfDUf3/mZeHm0wZnigP/iKJjUZhiMnzvtdLTjwytos8NLazWBXhhfBiStkF5fLCslT557bj+rH60Phl31g9G6SjCf7yVSFM7cGzKjVX97LszCxoWPFV6RQRIFenxOjAohaQs+pfT1aanfTckr2yKrV2inV4oI/86apk+XX/OP6/Q6vJLSyXIbNW6D29vv3jaEloGyBWRXghvJja7swCmfXVPlmXdko/Vp8TaoPHGwa2lzHJEU5VB5JVUCabDp+WNQfz5NvUvJ/szpwSGyxX9ajtYUmKtM4Gaq5EBdGZS/bqhe+UIR3D5H9+2dMUgRrm9/Z3h+W/vtgn/dqHyoL7h4uVFTpbeJkzZ4688MILkp2dLb1795bXXntNBg0adN7nf/755/L000/L0aNHpXPnzvK///u/Mn78+CZ9L8KLdWw9dkbeWJ0m3+zLbVQfcm3vdnJF9yi9oWBr1oeofypqjRrVLrXxpDqOnipt9By1C/NlncP1Sq5q0bgoNge0BLUc+7x1R+SVbw7qeiU18+vBMUlyz6hOzAKDQ13z2nd6r7LnJvWQW4d2ECsrdKbw8umnn8rkyZNl7ty5MnjwYHn55Zd1OElNTZXIyJ9W8q9fv15Gjhwps2bNkmuuuUY++ugjHV62bdsmKSkpP/v9CC/Wo3YO/mxLhvxj6/GGdTmUsABvHRTUlgP9E8L01vAtFWbUmivHTpXq7616gtQQ0K7j+T/ZnVl9O7WT8ZCObXVYGZAQxoeZhWWcLpX/t2i3rj9QOkcGyl9+1VO//4CWdjCnSK54aY14urvJ9/9vrP6dZ2WFzhReVGAZOHCgzJ49Wz+22WwSHx8vDz74oDzxxBM/ef4NN9wgJSUlsmTJkoZzQ4YMkT59+ugA9HMIL9b+63fl/hy9PPbK/bmN1kSp39snMTxQ15aoqvyIIB9pG+Cj/8H7eLmLt4e7XoDMLnYprayR8soaKams0YW1OYXletn9nIJyOXKqRM+CqlaDzD+i6nDUNNrBHdvq4QPV+xNMEadLUb8y1YJhaq0iNUyohjXvGpEoj12ZzGrHaFHPL90vr68+JGO7Rcrbtw0Uqytsxue3QzdCqayslK1bt8r06dMbzrm7u8vYsWNlw4YN53yNOv/oo482Ojdu3DhZtGjROZ9fUVGhj7N/eFiT6tG4She8xujl87fUDd+oYZzt6fl6ptK+rEJ9tIQAbw9d19AtJkh6xoVK77gQ3bvD6rauTRXrTuoTq3dJV7UIqkfwre+O6MLev/22t/SKs9Y0fxg3AWDxjhP6/nV9Y41ujtNxaHg5efKk1NTUSFRUVKPz6vH+/fvP+RpVF3Ou56vz56KGl/785z+3YKthBqpoVw3VqKN+80LVpX8or1gf6adL5WRRpe5VOV1aqYeBqqrt+lbx8/bQC+OpjQ3bBvro5eHVLsyRwT7SoW2AXtdDnWNWCc4n1N9b/vqb3nqNnicW7NJDjL98fb08MCZJT6tmmwFciu+PntY7ouu9zLo1/kyEg8NLa1C9Omf31KieFzUsBdeial06hAfoQ+2yDLQW9X77+uE28vTi3bJkZ5a8uuKgXt9HbXnROYoZZrg4n23O0LcTesUwHHkODv3TIDw8XDw8PCQnJ6fRefU4Ojr6nK9R55vzfB8fHz02dvYBAK2pTYC3zL65n94pPdTfS/acKJSJs9fKR5vSdY0M0Byqnu+LXVn6/g0D+WO81cOLt7e39O/fX1asWNFwThXsqsdDhw4952vU+bOfryxfvvy8zwcAZzGxdzv5+uGRehac2ofmyYW75P4Pt0nBj2apAReiCsIrqm2SHBVkua1SWorDB2XVkM5bb70l7777ruzbt0/uu+8+PZtoypQp+utqGvXZBb0PPfSQLF26VF588UVdF/Pss8/Kli1bZNq0aY5uKgBcsshgX3l3yiB5cnxXPTtNbQ9x9StrZPPR2v27gJ/z6eZ0ffvbgfHU3RlV86KmPufl5cmMGTN00a2a8qzCSX1Rbnp6up6BVG/YsGF6bZennnpKnnzySb1InZpp1JQ1XgDAGai9qu4e2UkXlP/+4+16McMb3twgD13eRab9IonNN3Feal0ptSidWtpBbY+Cc2N7AABwIDWFf8ai3bJge6Z+PDyprbx6Y189yw34sRmLd8t7G47JNb1idB2VKylsxuc3c/kAwIHUlhF/u6GPXgNGTc9Xe3ZNeHWtXp8IOFtZZY0srAu5FOpeGOEFAFrB9f3i5F/ThusVoLMLy/Uw0ry1R5iNhAaLd2RKUXm1tA/zl+Gdwo1ujlMjvABAK1HrviyeNkKv3aG2n1C7VU/7eLseWoJrUyH23Q3H9P1bhyTouimcH+EFAFp5GGn2TX3lmYnd9YZ7X+zMkmtnr5UDOUVGNw0GUsOIamsTtUfbbwbEGd0cp0d4AYBWpqa/ThmeKJ/eM0Sig33lcF6JXDdnnXxZtzAZXE99r8uk3rF66wlcGOEFAAzSPyFMlvx+hJ6BpHY6Vwvavfh1qt6UD64jt7BcvqoLrrcOTTC6OaZAeAEAA4UH+uhF7e4akagfv7YyTe5+f4sUlbMqr6v4+PsMXQPVP6GNpMSGGN0cUyC8AIAT7JL+1DXd9XRqb093+WZfrh5GOpxXbHTT4GDlVTXy/sbaIaPJ9Lo0GeEFAJxoOvXn9wzVdTCH8kpk0px1smp/rtHNggMt2p4pJ4srpF2Ir4zvGWN0c0yD8AIATqR3fKj868HhMiChjV7z4453N8vrq9NYD8aCVG3TW98d1vfvGJEoXh58JDcVVwoAnExkkK98NHWI3DSovajM8vzSVPn9Jzv0EAOsY+X+XN3DFuTrKTcOam90c0yF8AIATkjVvsy6vqf813Upej2Yf/9wQq/Kq2amwBr+XtfrcvPg9nr9HzQd4QUAnNgtQxLk/TsHS6i/l/xwvECunb1O7zwMc9uRkS/fHzktXh5uMmVY7UwzNB3hBQCc3NBObWXR/f/ZF+k3czfI0t0saGdms1em6dtre8dKdIiv0c0xHcILAJhAh/AAWXD/cLmsc7iUVdXIvR9skzmrKOQ1I9Vz9s2+HFHbF90/ppPRzTElwgsAmESIn5e8c/tAuX1YB/34hWWp8sinFPKatddlYu920iki0OjmmBLhBQBMtqDds9f2kOeuSxEPdzdZtOOE3PzWRskrqjC6aWgCtfni0j3Z4uYmMm1MktHNMS3CCwCY0K1DEvS2AsG+nrItPV+vyKs+GGGOXhe1IF3nqCCjm2NahBcAMKkRncNl4QPDJTE8QDLzy+RXb6yX5XtzjG4WzkOFyy/rCq1//4vORjfH1AgvAGBiqmZi4f3DZFin2p2p1aaOb357iEJeJ/T80v160cEJvWIkOZpel0tBeAEAkwv195Z37xikFztTH46zvtovf/zHTqmoppDXWWw4dEpWpebpBQf/eGWy0c0xPcILAFiA2hfnv69LkWcmdtdTcP+x9bjc8vYmvekfjKV6wf6ydL++r7Z8UNPecWkILwBgEW5ubjJleKK8M2WQ3i9n89EzMmk2hbxGW7o7W37IyBc/Lw958HJmGLUEwgsAWMyoLhGy8P7h0qGtf0Mh79d7so1ulktSQ3fPL0vV96delqg33cSlI7wAgAUlRQbKogeGy/Ck2kLeez7Yyoq8Bpi39qgcOVkiEUE+MnVkR6ObYxmEFwCwcCHv/CmDZPLQBF3Iy4q8rSunsFxeW3lQ33/iqq4S5OtldJMsg/ACABYv5J05KaXRirw3/n2j5BaWG900y5v15T7d69Wvfaj8sm+s0c2xFMILALjIirzv3zFI74+0IyNfJs1ZpzcIhGNsPnpaB0W1DcCfr00RdzUFDC2G8AIALmJYUrgsfmC4dIoIkKyCcvn13PXy5a7aFV/RskW60xfs0vdvHBgvPeNCjG6S5RBeAMCFqDVG1JYCakZSeZVN7v9wm7zyzUEKeVvQnJVpkpZbLOGBPvKnq7oa3RxLIrwAgIsJ9vWSebcPlLtGJOrHL31zQB74aJsUV1Qb3TTTU2vqvL76kL4/c1IPXTSNlkd4AQAXpIp3n7qmuzz/q17i5eEmX+7Kll/OWSeH8oqNbpppVdfY5E//3CnVNruM6xElV6dEG90kyyK8AIAL++3AePn0nqESFewjB3OL9Yq8y1jQ7qLMXpUmO48X6NWNn5uUolc8hmMQXgDAxfVr30aWPHiZDEoM00NH97y/Vf66LFVqbNTBNNWWo6fl1RW1a7qo4BIZzEq6jkR4AQDoFWA/vGuw3DE8saEXYcr8zXKmpNLopjm9wvIqeeiTHaKynlrP5TrWdHE4wgsAoGFBuxkTu8srN/YRXy93WXMgTybOXst6MBegZmn9v4W79R5S8WF+ukgXjkd4AQA0MqlPrN7YsX2Yvxw/UybXv75e3ll3hOnU5zBv3VH59w8ndAH0yzf0ZQuAVkJ4AQD8RLeYYPn3tBFyZfcoqayxyZ//vVfufn+r5JcyjFRv/aGT8j9f7tP3nxzfTfontDG6SS6D8AIAOKcQfy9589b+8uzE7uLt4S7L9+bI+Fe+k63HTourU8NE0z7arouaVZ3LHcM7GN0kl+Kw8HL69Gn53e9+J8HBwRIaGip33nmnFBdfeP2A0aNH66llZx/33nuvo5oIAPgZ6vfw7cMTZcH9w6RDW385UVAuv31zo8xZleays5EKSqvkjnc2y+mSSkmJDZZZ1/dkWrRVwosKLnv27JHly5fLkiVLZM2aNXL33Xf/7OumTp0qWVlZDcfzzz/vqCYCAJooJTZE/v3gCLm2dzsdWl5Yliq/fXODHD1ZIq6kvKpGpr63RVJziiQyyEfevHWA+Hp5GN0sl+OQ8LJv3z5ZunSpvP322zJ48GAZMWKEvPbaa/LJJ5/IiRMnLvhaf39/iY6ObjhUzw0AwHiqGFXNRHr+170k0MdTth47I1e/8p18sPGYSxTzqtD28Cc75PujpyXIx1PevWOQxIb6Gd0sl+SQ8LJhwwY9VDRgwICGc2PHjhV3d3fZtGnTBV/74YcfSnh4uKSkpMj06dOltLT0gs+vqKiQwsLCRgcAwDHU8MhvB8TLVw9dJoMTw6SsqkaeWrRbbn9ns2QXlIuVl/5/7LMdsnRPtq7/+fvkAbqoGRYKL9nZ2RIZGdnonKenp4SFhemvnc/NN98sH3zwgaxatUoHl/fff19uueWWC36vWbNmSUhISMMRHx/fYj8HAODc4sP85eOpQ+Tpa7qLt6e7fHsgT6546VvdC2OzWC1MVY1NHv50hyzacUI83d3k1Zv6yNBObY1ulktrVnh54oknflJQ++Nj//79F90YVRMzbtw46dmzp66Zee+992ThwoVy6FDtDp3nokJOQUFBw5GRkXHR3x8A0HTu7m5y54hE+eLBEdI7LkSKyqt1L8yv566X1OwisUqNy4MfbZclO7P0Bpav/66fXJUSY3SzXJ5nc5782GOPye23337B53Ts2FHXquTm5jY6X11drWcgqa81laqXUdLS0qRTp07nfI6Pj48+AADG6BwVJAvuHy7vbTiq90Talp4vE179Tu4e2VGm/SJJ/L2b9VHjNE4WV8jd723RP48aKnrjln5yebcoo5uF5oaXiIgIffycoUOHSn5+vmzdulX69++vz61cuVJsNltDIGmKHTt26NuYGFIuADgztcLslOGJclVKtDyzeI98vTdHXl99SBZsy5Q/jkvWa6GonhqzOJhTJHe8u1kyTpdJiJ+XzL2lP0NFTsTN7qAS8auvvlpycnJk7ty5UlVVJVOmTNEFvB999JH+emZmplx++eV6aGjQoEF6aEh9bfz48dK2bVvZuXOnPPLIIxIXFyfffvttk7+vKthVtS9qCImZSgBgjGV7suW5JXv19gKKWg/lqQndZUhH5w4A6iPx8y3H5Zl/7dHFyAlt/WXe7QOlU0Sg0U2zvMJmfH47rC9PzRqaNm2aDihqltGvfvUrefXVVxu+rgJNampqw2wib29v+eabb+Tll1+WkpISXXirXvPUU085qokAAAcZ1yNaRnWJkHfXH5XZK9Nkd2ah3Pj3jfrcQ2M7S7/2bZxy8bmnFu/WexUpI5LC5dWb+kpYgLfRTUNr9bwYhZ4XAHAup4or5KVvDsjH32c0rMo7skuE/P4XSXo/IKNXp1Ufg4t3nJD/+mKvnCyu1ENgj13ZRe4d2clUQ12u9PlNeAEAtIr0U6Uye9VB+ee2zIYQo2Yp3T68g4zvGSM+nq2/Uu329DPy/NJU2XD4lH7cKSJAnv91bzZZNADhhfACAE4dYl5fnSYLtmdKZbVNnwsP9JZf9Y/Thb1dox37u1t97G1LP6OHs1al5ulzPp7u8vvLO8vUyzrqdWvQ+ggvhBcAMMVw0iebM+T9Dccku/A/q/N2jQ7SPTGjkyMkpV1Iiw3d5BaVy5c7s/TwldqbSFFDRNf3jdXBRS28B+MQXggvAGCqFWxX7MuVRdszZeX+XKmsqe2Nqe+RGdYpXHrFhUif+FDp3i64yevGnCmplJ2ZBXpoSPWw/JCR3/A1Xy93vcnk/aOTpEN4gEN+LjQP4YXwAgCmpGb8LN2TpcPMurSTUlJZ85PnRAT5SHwbPwkP9JFAX08J8PaUGrtdKqpsUlJRLVkFZXKioFzyiip+8loVgn7VL06u6xur12+B8yC8EF4AwPRUPcyWo6dly7EzsvN4vvxwvOCcgeRCOoYHSEpsiF5g7hddIyUq2Ndh7YUF1nkBAOBSqMLZYUnh+lDU39oFZVV61duMM6VyprRSisurdW+Lh7u7fr6/t4dEh/hKuxA/ad/Wn94ViyK8AABMQa0HE+rvrY+ecSFGNwcGYj4YAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcILAAAwFcvtKq22TFcKCwuNbgoAAGii+s/t+s9xlwovRUVF+jY+Pt7opgAAgIv4HA8JCbngc9zsTYk4JmKz2eTEiRMSFBQkbm5u4gpJVQW1jIwMCQ4ONro5To1r1Txcr6bjWjUd16rpXO1a2e12HVzatWsn7u7urtXzon7guLg4cTXqje0Kb+6WwLVqHq5X03Gtmo5r1XSudK1CfqbHpR4FuwAAwFQILwAAwFQILybn4+MjzzzzjL7FhXGtmofr1XRcq6bjWjUd18qFCnYBAIC10fMCAABMhfACAABMhfACAABMhfACAABMhfBiQv/93/8tw4YNE39/fwkNDW3Sa26//Xa94vDZx1VXXSVWdzHXStWwz5gxQ2JiYsTPz0/Gjh0rBw8eFKs7ffq0/O53v9OLYalrdeedd0pxcfEFXzN69OifvK/uvfdesaI5c+ZIhw4dxNfXVwYPHizff//9BZ//+eefS9euXfXze/bsKV9++aW4iuZcq/nz5//kPaRe5wrWrFkjEydO1CvKqp970aJFP/ua1atXS79+/fQMpKSkJH39XBHhxYQqKyvlN7/5jdx3333Nep0KK1lZWQ3Hxx9/LFZ3Mdfq+eefl1dffVXmzp0rmzZtkoCAABk3bpyUl5eLlangsmfPHlm+fLksWbJE/2K9++67f/Z1U6dObfS+UtfPaj799FN59NFH9bTVbdu2Se/evfV7Ijc395zPX79+vdx00006AG7fvl2uu+46fezevVusrrnXSlGB+ez30LFjx8QVlJSU6Oujwl5THDlyRCZMmCBjxoyRHTt2yMMPPyx33XWXLFu2TFyOmioNc3rnnXfsISEhTXrubbfdZp80aZLdVTX1WtlsNnt0dLT9hRdeaDiXn59v9/HxsX/88cd2q9q7d69aMsG+efPmhnNfffWV3c3NzZ6ZmXne140aNcr+0EMP2a1u0KBB9gceeKDhcU1Njb1du3b2WbNmnfP5v/3tb+0TJkxodG7w4MH2e+65x251zb1Wzfk9ZmXq39/ChQsv+JzHH3/c3qNHj0bnbrjhBvu4cePsroaeFxeiuhsjIyMlOTlZ90ScOnXK6CY5HfWXTXZ2th4qOnuvDdX1vWHDBrEq9bOpoaIBAwY0nFPXQO0VpnqfLuTDDz+U8PBwSUlJkenTp0tpaalYrfdu69atjd4T6rqox+d7T6jzZz9fUb0PVn4PXey1UtTwZEJCgt6EcNKkSboHED/lqu8rl9iYEecfMrr++uslMTFRDh06JE8++aRcffXV+k3v4eFhdPOchgouSlRUVKPz6nH916xI/Wwq2J7N09NTwsLCLvhz33zzzfpDR43Z79y5U/70pz9JamqqLFiwQKzi5MmTUlNTc873xP79+8/5GnXNXO09dLHXSv0xNW/ePOnVq5cUFBTIX//6V12npgKMK26yeyHne18VFhZKWVmZrtFzFfS8OIknnnjiJ0VrPz7O94+/KW688Ua59tprdeGgGntXNQ2bN2/WvTFm4+hrZSWOvlaqJkb95afeV6pm5r333pOFCxfqgAw0xdChQ2Xy5MnSp08fGTVqlA6+ERER8uabbxrdNDgxel6cxGOPPaZnBF1Ix44dW+z7qf+W6upPS0uTyy+/XMzEkdcqOjpa3+bk5OjZRvXUY/XL1Wyaeq3Uz/3jgsrq6mo9A6n+mjSFGl5T1PuqU6dOYgXq34nqnVTvgbOpx+e7Nup8c55vFRdzrX7My8tL+vbtq99DaNr7Kjg42KV6XRTCi5NQf2moo7UcP35c17yc/QFtFo68VmpYTf2CWLFiRUNYUV2yqu6jubO7zHSt1F+/+fn5ul6hf//++tzKlSvFZrM1BJKmUDMgFDO+r87H29tbXxP1nlC9loq6LurxtGnTzns91dfVbJB6ahaXOm9lF3OtfkwNO+3atUvGjx/v4Naaj3r//HjK/XIXeF+dk9EVw2i+Y8eO2bdv327/85//bA8MDNT31VFUVNTwnOTkZPuCBQv0fXX+D3/4g33Dhg32I0eO2L/55ht7v3797J07d7aXl5fbray510r5y1/+Yg8NDbUvXrzYvnPnTj1LKzEx0V5WVma3squuusret29f+6ZNm+xr167V74+bbrqp4evHjx/X10p9XUlLS7PPnDnTvmXLFv2+UterY8eO9pEjR9qt5pNPPtEzzubPn69nZt199936PZKdna2/fuutt9qfeOKJhuevW7fO7unpaf/rX/9q37dvn/2ZZ56xe3l52Xft2mW3uuZeK/Vvc9myZfZDhw7Zt27dar/xxhvtvr6+9j179titTv0eqv+dpD6O//a3v+n76veWoq6Tul71Dh8+bPf397f/8Y9/1O+rOXPm2D08POxLly61uxrCiwmpac/qjf7jY9WqVQ3PUY/VFESltLTUfuWVV9ojIiL0L9CEhAT71KlTG36ZWFlzr1X9dOmnn37aHhUVpX8JX3755fbU1FS71Z06dUqHFRXygoOD7VOmTGkU8lRAOfvapaen66ASFhamr1NSUpL+pVpQUGC3otdee83evn17u7e3t54OvHHjxkZTxtV77WyfffaZvUuXLvr5anrrF198YXcVzblWDz/8cMNz1b+58ePH27dt22Z3Berf0rl+P9VfH3WrrtePX9OnTx99vdQfC2f/7nIlbup/jO79AQAAaCpmGwEAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAAFMhvAAAADGT/w+ztl3zq+FbdgAAAABJRU5ErkJggg==", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = -1.5\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "ac35388f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "5-element Vector{PyCall.PyObject}:\n", + " PyObject \n", + " PyObject \n", + " PyObject \n", + " PyObject \n", + " PyObject " + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew = newton_step(xguess[end])\n", + "xguess = [xguess xnew]\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "markdown", + "id": "7cf57032", + "metadata": {}, + "source": [ + "## Let's now test out a different starting point for newton to motivate the need for \"Globalization Strategies\" to make newton work better and more generally!" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5792cd59", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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gQl3dCz0vAABnlHm6TCqqbbrMweiZRk7X83I227dv18NJVjagPrwczC+VU6VVRjcHAICzFusmRQYavjWAw3teSkpKJD09vfHx4cOHdRgJCwuTjh076iGfrKwseeedd/TXX3zxRUlMTJSePXtKRUWFvPnmm7Jy5Ur58ssvxcraBXhL16hAOZBXooeOrkqJNrpJAAD8uFjXCYaMHB5eNm/eLFdccUXj40cffVTf3nbbbTJv3jy9hktGRkbj16uqquSxxx7Tgcbf31969+4tX331VZP/hlUN7NROh5fNR04RXgAATmW/ExXrOjy8qJlCau2Sc1EB5kyPP/64PlzRwIQw+fC7TOpeAABOJy2nLrz0iHWO8OL0NS+uQvW8KDuzCtmkEQDgNKpqbI0zjZJjgsUZEF6cRMcwf4kM8pHqWrvsOMYmjQAA53Awv0RvIBzk6yntQ3zFGRBenITaFuDMrQIAAHCmIaPuMUFOs4UN4cWJDEioW6yOTRoBAM5ib07dtjvdnWTISCG8OJHGnpcjp/RqhgAAOE3PS6xzFOsqhBcnkhIbLP7eHlJUUSNp9dPSAAAw0r7s/w4bOQvCixPx9HBv3Odow6GTRjcHAODiCsqqJKeoQt/v5iRrvCiEFycztDPhBQDgHPbVDxl1aOcnQb5e4iwIL05maOdwfbvxMHUvAABj7ct2vmJdhfDiZHrFhei6l4KyaupeAACGSst1rpV1GxBenIwXdS8AACext75YN9mJinUVwosTou4FAGA0m83euCEjw0a4IOpeAABGyzxdJmVVteLt6S6dwv3FmRBenLzupaHSGwAAI4aMukUH6qU8nIlztQYadS8AAGdZWTc52rmGjBTCi5MaVj90RHgBABhhX/2eRs4200ghvDh50S51LwAAY3eTDhZnQ3hxUqlxIRLg7SGF5dS9AADaVnlVrRw+WeqU06QVwouTou4FAGCU/bnFYreLhAd4S2SQjzgbwosJpkyvO0h4AQC0nT312wKktHe+ISOF8OLEhnepX+/l0EmpqbUZ3RwAgIvYfbxQ3xJecFF1LyF+XlJcWSPfHyswujkAABex+3hdz0vP9iHijAgvTszD3U1GJNX1vqw9wNARAMDxam122Ve/QF1KLD0vuAgjkyL17dr0fKObAgBwAYdPlEp5da34eXlIYkSAOCPCi5O7rGuEvt2WUSAllTVGNwcA4CL1Lj1ig/QIgDMivDi5+DB/6RjmLzU2uy7cBQDAkfY4eb2LQngxgZH1vS/fHDhhdFMAAC5SrJvipDONFMKLCVyWVBde1qYTXgAAjmO32xuHjXoSXnAphneJEDXsmJ5XIjmFFUY3BwBgUTlFFXK6rFrXunSLdr5tARoQXkwgxN9LenUI1ffpfQEAOMrurLoho65RgeLr5SHOivBiEiMb13thyjQAwHXrXRTCi+nWezkhNpvd6OYAAKy8LUAs4QWtYEBCOwn08ZQTJVWyq/7NBQCAK20L0IDwYhLenu4ysn7W0eo0ho4AAK2rsKxasgrK9X2GjdBqRifXDR2tSsszuikAAIvZnV3Xqx8f5qc3BXZmhBcTGZ0cpW+3ZxbIqdIqo5sDALDiyrqxzj1kpBBeTCQmxFe6xwSJ3a5W22XoCADgejONFMKLyVzRva73ZdU+ho4AAK3HDCvrNiC8mMzobnV1L2sOnJBapkwDAFpBWVWNXsVdSY1j2AitrH9COwny9dQ1LzuOFRjdHACARepdbHaR6GAfiQ72FZcOL2vWrJHrr79e2rdvL25ubrJw4cILvmb16tXSv39/8fHxkaSkJJk3b54jm2g6Xh7ucln9LtNMmQYAtIYdx+qGjHrF1W1F49LhpbS0VPr06SOzZ89u1vMPHz4s48ePlyuuuEK2b98uDz/8sNx1112ybNkyRzbTtLOOVjNlGgDQCnZm1YWX3h2cf8hI8XTkf/zaa6/VR3PNmTNHEhMT5YUXXtCPe/ToIWvXrpW///3vMnbsWAe21Jx1LzuyCiWvuEKigpy/iw8A4Ly+ry9D6GWS8OJUNS/r16+XMWPGNDmnQos6fy6VlZVSVFTU5LC6qGBf6dMhRE+ZXrmX3hcAwMUrrqiWQ/ml+n5vExTrOl14ycnJkejo6Cbn1GMVSMrL65Ys/qFZs2ZJSEhI4xEfHy+uYEyPuuu0fE+u0U0BAJjYrqy6P/rjQv0kPNBHzMCpwsvFmDFjhhQWFjYemZmZ4gqu6hnduMu0muIGAMDF2JlVYKp6F6cLLzExMZKb27QnQT0ODg4WPz+/s75GzUpSXz/zcAXJ0UF6/4nKGpus2X/C6OYAAMw+06gD4eWiDBs2TFasWNHk3PLly/V5NKWmnl/VI0bf/2ovQ0cAgEucaWSSadIODy8lJSV6yrM6GqZCq/sZGRmNQz5TpkxpfP69994rhw4dkscff1z27dsnr776qnzyySfyyCOPOLKZpjUmpW7K9Mp9eay2CwBoscKyajl6skzf72WSYl2Hh5fNmzdLv3799KE8+uij+v7MmTP14+zs7MYgo6hp0p9//rnubVHrw6gp02+++SbTpM9hcKcwvW25Wm13y9HTRjcHAGDSXpeEcH8J8fcyujnOsc7L6NGjxa7m857D2VbPVa/Ztm2bI5tlGZ4e7vKT7lGyYFuWLN+TI4MTw4xuEgDARHbUF+uaqdfF6Wpe0HJXpfx3yvT5giIAAD+0s75Y10wzjRTCi8ld3i1SvD3c5cjJMjlQvyMoAABW3NOoAeHF5AJ9PGVk/UaNX+zMMbo5AACTyC+ulKyCcnFzE0mNM9cyI4QXCxjXK1bfLtmZbXRTAAAmsT2zrt6la1SgBPmap1hXIbxYwFU9osXLw03ScoslnaEjAEAzbM+sm6XaN95cQ0YK4cUC1PS2EUkNQ0f0vgAALmxbRl3PS7+O7cRsCC8WGzr6nPACALgAtbBpQ7EuPS8wzNUp0eLp7ib7corlUD5DRwCAc1MlBiWVNeLv7SHdooPEbAgvFhHq7y3DG4aOdjHrCABw4XoXtb6Lh7ubmA3hxULG96rbqPHzHQwdAQCsWe+iEF4s5KqUGJ2g92QXyZETpUY3BwDg5NOk+5qw3kUhvFhIWIC3DO8Sru//5/vjRjcHAOCESipr9NIaSj/CC5zBDX3a69uF27PY6wgA8CM7jhWI+niIC/WTqGBfMSPCi8VckxojPp7ucjC/VHYfLzK6OQAAJ6136dvRnL0uCuHFYtQSz2N61O00vXBbltHNAQA4ab1LP5MOGSmEFwua2C9O3/77++N6ISIAABRVTvDfmUaEFziRUd0iJdTfS/KKK2XDoZNGNwcA4CSOnS6XEyWVej+8nu1DxKwILxbk7eneuF0AQ0cAgAZbM+oWp0uJDRZfLw8xK8KLRU3sG9e42m5Fda3RzQEAOIFNR07p24GdwsTMCC8WNTChnZ4Gp+bzr9ibZ3RzAABOYPOR042fEWZGeLEod3c3mdC3bs2Xz7ZkGt0cAIDBiiqqGxenG9CJ8AIn9cuB8fr26/35klNYYXRzAAAG2pZRtzhdxzB/iQoy5+J0DQgvFpYYESCDO4WJmi39r63HjG4OAMBAmxvrXczd66IQXizulwM76NtPN2eyXQAAuLDNjfUu5i7WVQgvFje+d6wEeHvIkZNl8t3hutQNAHAt1bW2xpV16XmB0/P39pTr6zdr/GQzQ0cA4Ir2ZhdJeXWtBPt6SlJkoJgd4cWFCneX7MyW4opqo5sDAGhjm+qHjAYktNOzUc2O8OIC+ncMlS6RATp1/+f7bKObAwBoY1uOWmNxugaEFxfg5uYmkwbV9b58tCnD6OYAANqQ3W63zOJ0DQgvLuIXA+L1nkc7jhU2Fm0BAFxjM8a84rrNGPvEm3cn6TMRXlxEWIC3XFe/WeO7648a3RwAQBv5rn6mqdpF2sybMZ6J8OJCbh2WoG//s+O4nCqtMro5AIA2sPHwSX07pLM16l0UwosL6RsfKqlxwVJVY9OL1gEArG9jfc/L0MRwsQrCi4sV7k4Z2knff2/jUbGpfQMAAJaVXVguR0+WiZodbYXF6RoQXlyMWrBOLVKUeapcb9gIALCujYfqel1S40IkyNdLrILw4mL8vD0aF617e/0Ro5sDAGiLepdE69S7KIQXF3Tr0ARxcxNZnZYv6XnFRjcHAOAgG+p7XoZYqN5FIby4oE4RAXJVj2h9/81vDhvdHACAA+QWVcjhE6X6j9VB9LzACu6+vLO+nb8tS/KLK41uDgCglW04VDdklBIbLCF+1ql3abPwMnv2bOnUqZP4+vrKkCFD5Lvvvjvnc+fNm6dnxZx5qNehdanNudTUaTVt+l1qXwDAulOkO1tryKhNwsvHH38sjz76qDz99NOydetW6dOnj4wdO1by8vLO+Zrg4GDJzs5uPI4eZUXY1qZCYUPvy7sbjkp5Va3RTQIAtKKNh6xZrNsm4eVvf/ubTJs2TaZOnSopKSkyZ84c8ff3l7lz5573gzUmJqbxiI6uq89A6xrbM0biw/zkdFm1fLb1mNHNAQC0krziCjmYX1fvMpjw0jJVVVWyZcsWGTNmzH+/obu7frx+/fpzvq6kpEQSEhIkPj5eJkyYILt37z7ncysrK6WoqKjJgebxcHeTO0ck6vv/980hqWXROgCw1H5G3WOCJdTfW6zGoeHlxIkTUltb+6OeE/U4JyfnrK9JTk7WvTKLFi2S9957T2w2mwwfPlyOHTt7z8CsWbMkJCSk8VCBB82n1nwJ9feSIyfLZPGO40Y3BwDQCtYdtO6QkVPONho2bJhMmTJF+vbtK6NGjZL58+dLZGSkvP7662d9/owZM6SwsLDxyMxkz56WCPDxlLtG1vW+vLwynS0DAMACvk0/oW9HJkWIFTk0vERERIiHh4fk5uY2Oa8eq1qW5vDy8pJ+/fpJenr6Wb/u4+OjC3zPPNAyU4Z30lsGpOeVyBe7zt4jBgAwh8xTZXo/I1UaYKWdpNssvHh7e8uAAQNkxYoVjefUMJB6rHpYmkMNO+3cuVNiY2Md2FLXFuzrJXc09r4coPcFAExs3cG6Xhe1HIaV9jNq02EjNU36n//8p7z99tuyd+9eue+++6S0tFTPPlLUEJEa+mnwzDPPyJdffimHDh3SU6tvueUWPVX6rrvucnRTXdrU4YkS5OMp+3KK5cs9TXvKAADmsTa9rt5lhEWHjBRPR3+DSZMmSX5+vsycOVMX6apalqVLlzYW8WZkZOgZSA1Onz6tp1ar57Zr10733Kxbt05Ps4bjhPh7yW3DO8krq9LlpRUHZGzPaD1lHQBgHjabXdZZvN5FcbPb7ZYaI1BTpdWsI1W8S/1Ly5wurZKR/7tSSqtq5bWb+8u1vRiqAwAz2XO8SMa99I34e3vI9plXi7en083LaZXPb/P8VHC4dgHecudldavuPr8sTWpqbUY3CQBwEbOMhiSGmSq4tJR1fzJclGmXJUp4gLccOlEqn2xm1V0AMJO19eHFyvUuCuEFTajK9Ok/SdL3X/xqP3seAYBJVNbUNq6sO7Ir4QUu5qYhHfWeR3nFlTL328NGNwcA0AzbMgqkvLpWIgK9JTk6SKyM8IIf8fH0kMeuStb353x9UBfyAgDMUe8yvEuE5WeLEl5wVjf0aS8pscFSXFEjLyxPM7o5AIAL+Hp/vuWnSDcgvOCs3N3dZOb1dWvrfLAxQ3YfLzS6SQCAczhRUik7jtX9nh6VHClWR3jBOQ3tHC7X92kvareAP/x7t1hsSSAAsIw19b0uPWKDJTrYV6yO8ILz+v247uLn5SGbjpyWRduPG90cAMBZrE6rCy+jXaDXRSG84LxiQ/wap07/ecleKamsMbpJAIAz1NrssuZAXXi5IjlKXAHhBRd012WJkhDur6dOv/AlxbsA4Ex2HCuQgrJqCfL1lP4dQ8UVEF7QrKnTz0xI1ffnrTsiWzNOG90kAMAPhowu6xohnh6u8bHuGj8lLtmobpHys/5xomp2H/9sh17JEQBgvNX1xbqju7nGkJFCeEGzPTU+Ra/cmJ5XIrNXphvdHABweSf1FOkCl5ki3YDwghbtOv3HG+qGj15dfVD2ZhcZ3SQAcGnfHDihe8RdZYp0A8ILWmRcrxgZ2zNaamx2eeTj7VJRzfARABhldVqeS02RbkB4QYuo/TKenZgq4QHesi+nWJ5byuwjADBCTa3tjHoXwgtwXlFBvvLcL3rr+2rX6YbkDwBoO5uPntZTpNv5e8mAhHbiSggvuChX9oiWKcMS9P3ffLpD8osrjW4SALiUr/bk6tsruke5zBTpBq7106JV/X5cD+kWHag3BHvww626CxMA4Hh2u12W760LL1enRIurIbzgovl6ecirN/eXAG8P2XDolDy3jPoXAGgLB/JK5OjJMvH2dJfLurpWvYtCeMElSYoKkud/2Ufff2PNIVmyM9voJgGA5S2vHzIa0SVcAnw8xdW43k+MVjeuV6zcc3lneX3NIfnNp99LxzB/SY0LMbpZcCA1RJhfUil5RZVSWF4txRU1UlJZd6umz9vsdZvFqa5tu95iwl38vD3F39tDH8G+XhIZ5KMPNXPN1cbrgdYKL1elxIgrIrygVfx2bLLsyS7SCybdMW+TLHxghLQP9TO6WbgEhWXVcvBEiRzKL5WD+SVy5ESpHC+skJzCcl2grQJKa3BzEwkP8JGOYX7SOTJQEiMCpHNEgHSNVvcDxcPdrXW+EWAReUUVsj2zblXdK3u4zpYAZyK8oFWov5xn39xffvHaOtmfW6IDzKf3DpMgXy+jm4YLUL0j2YUVsjOrUHZlFdbfFulC7PPxdHfTPSchfl66JyXQ11Pvauvr6SHu7m6iOlPcVTIRkcpqm5RV10p5VY2UVdXq6Z2q50Ytba5CkPpe6tiaUfcLuYGqp+oZFyJ9OoRIrw6hMrhTmMSEuM4qosDZrNhXtzxFn/hQl1pV90yEF7Qa9QE29/ZB8tNX1+kF7O55d4t+rAp74VxDPruPF8l3h0/JxsOnZFvGaTlZWnXW58YE+0rnyADpUt8jEtfOT2JDfPX58ECfS+4VUUNLJ0vrhp+OnCzVvTyHT6jbEh2CS6tqdTvV0UC1Z0SXCBneJVyGdQmXUH/vS2oDYNohox6u2euiuNnVn10WUlRUJCEhIVJYWCjBwcFGN8clqU3CJr+xQX/wXNk9Sl67ZYCuiIcxVEBQ/598m35Ch5WtR0/r/2/OpEJI16hA6a16OOJCdM1S1+ggCTSwEFCFrIP5pbrtqjdoW0aB7D5e2GS4SrV7UKd2MrZnjFzdM0biGKqExZVU1kj/Z5dLVY1Nlj18uSTHBIkrfn4TXuAQGw6dlNvmfieVNTYZ3ytW/nFjX4oy25CqSfnmQL6sTsvXt6fLqpt8PdjXUwYnhuljYKcwSYkNNkUPmarD2XD4pKxLPyHfHjypdzg/kwpe1/eJlYl94yTKRbvTYW2LtmfJQx9t13VhKx4bpbdssQrCC+HFKahtA6a9s1mqa+16Q8cXJ/WjB8ZB1D9jVaeybHeOrN6fp++fKcjHU0YkRehhFhVYkqODdF2K2WWcLJMv9+Ton1stld7w20z9aJd3i5Sf9e+gF/AyQzADmuPudzbLl3tyZfoVSfKbscliJYQXwovT+HJ3jjzwwVYdYEZ1i5Q5twwQP28+SFqD+qerZhx8sStHr69z7HR5k6/3bB+sd5od1S1K+nUMFS+L93yp3iYVYuZvPdak8Ff1Mv1qYLxMGdZJOob7G9pGoLWGjJb8+jJJaW+tzzjCC+HFqazZn6+Ld8ura2VgQjv555SB0i6AIsuLYbPZZWvGaVmyM0eW7srWU5cb+Hq5yxXJUXrfqcu7RegNNF2VKvpVIWb+1izJKqgLdap3XV2f24Z3ksuSIizR8wTXHDJKjAiQlRYbMlIIL4QXp7Pl6Cm5/a1NehGzhHB/+b/bBklSVKDRzTJNwe2mI6fki53Zupcl74xNMNWCbyqsjEuNkVHJkeLvzQTCH4Y9NYz29rqj8vX+/Mbzak+u+0cnyXW9Y6nFgmnc8+5mWbY7Vx64oov8dmx3sRrCC+HFKaXlFMudb2/SwxtqPZCXJ/eT0cmuO9XvQjNt1MwgNRykhkJOlFQ1qV8ZkxIt16bG6LoO6jmaR02/fnfDUfl08zHd/a6o1aDvHdVFfj4gTnw8uY5wXqX1Q0ZqEsTnvx4pPdtbbxVzwgvhxWmpRcnufW+LbDpyWnfj3zeqizx6VTf++hWR6lqbrDt4UvewqMBy5gwhVbehpgKrwmdVeMsH7cVT2xm8t+Go/N/aw3Kqfn2b6GAf+fWVXXVtjNVrg2BO//7+uPz6w23SKdxfVv1mtOWGjBTCC+HFqVXW1Moz/9kj72/M0I8HJLSTFyf1lfgwf5e8Fmr9FVXDohaeUh+sDdr5e+n1S67tFSvDOoczU6uVlVfVykebMvSGomqFYUV9MDx6dbJc1yuWmhg4lXvf3SJLd+fI/aO7yOPXWG/ISCG8EF5M4fMd2fLEv3ZIcWWN+Hl56P2RVDGl1feyUR+aqv5CFdyu2Junf/4GEYHeOrCozS6HJIbRI9VGAfLDjRnyyqr0xuE5te7N49ckM6wJpxkyGvCn5VJRbZPFD4607Ma3hBfCi6nW6fjtZ9/r+g6lb3yo/OGGnvrWSooqqmXVvjxZuitHLxynZl41iAry0fUrqodlUKcwy4c3Z/6AmLv2sN4dvaEmRk01f+q6FL09AmCUBduOySMff2/ZWUYNCC+EF9PNCPlwU4bMWrKv8UNjQt/2uiemQzvzDiWpjQZX7M3VM4TU0JBa66aBWsb+mtQYfQzo2I4hCiei6mBeXZUub68/ov8/8/Jwk6kjEuXBnySx0SgMMWXud3rJiUfGdJOHxnQVqyK8EF5MKaewQp5flib/2npMP1YfGj/tF6dng3Q2wV++KoSpPXhWpeXpXpYdWYWNK74qXSID5NrUWB1Y1AJyVv3ryUqzk55dvEdWpdVNsY4I9JHfXZMsvxjQgf/v0Gbyiipk6KwVek+vr387WhLCA8SqCC+EF1PblVUos77YK9+mn9SP1eeE2uBx0qCOckVypFPVgWQXlsvGQ6dkzYF8+Tot/0e7M6fGBcs1Pet6WJKirLOBmitRQfSZxXv0wnfK0M5h8uef9jJFoIb5vfnNIfnT53ulf8dQmX//CLGyImcLL7Nnz5bnn39ecnJypE+fPvLyyy/L4MGDz/n8Tz/9VJ566ik5cuSIdO3aVf73f/9Xxo0b16zvRXixji1HT8trq9Plq715TepDbujTXq5KidYbCrZlfYj6p6LWqFHtUhtPquPIybImz1G7MF/WNUKv5KoWjYtmc0BLUMuxz/32sPzjqwO6XknN/Ho3Y4kM6BIpnk/P/PELnn1WpLZW5A9/MKK5sJDrXv5G71X27ISecuuwTmJlRS34/Hb4cpwff/yxPProozJnzhwZMmSIvPjiizJ27FhJS0uTqKgfV/KvW7dOJk+eLLNmzZLrrrtOPvjgA5k4caJs3bpVUlNTHd1cOBE1hfrN2wbpnYM/2Zwpn205pleXfXPtYX2EBXjroKC2HBiQEKa3hm+tMKPWXDl6skx/b9UTpIaAdh4r+NHuzOrbqZ2Mh3YO12FlYEIYU5otSP1/qoYv1Q7p/2/hLl1/sPbwaRny7iuSVVQhcS/8uWlwmTlT5JlnjGwyLOBAbrEOLp7ubjK+d3ujm+NUHN7zogLLoEGD5JVXXtGPbTabxMfHy4MPPihPPPHEj54/adIkKS0tlcWLFzeeGzp0qPTt21cHoAuh58Xaf/2u3Jerl8deuS+vyZooDXv7JEYE6toSVZUfGeQj4QE+OuT4eLmLt4e7XoDMLnYpq6qViqpaKa2q1YW1uUUVOhjlFlbI4ZOlehZUjRpk/gFVh6Om0Q7pHK6HD1TvTzBFnC5F/cpUC4aptYpu+vJteWzt+/L1zdNlyFsviu9f/vzf4PLUU0Y3FSb33NJ98urqgzKmR5T+Q87qipyl56Wqqkq2bNkiM2bMaDzn7u4uY8aMkfXr15/1Neq86qk5k+qpWbhw4VmfX1lZqY8zf3hY96/fa3TBa6xePn9z/fCNGsbZllGgZyrtzS7SR2sI8PbQdQ09YoOkV4dQ6dMhRPfusLqta1PFuhP6xuld0v/UPUpeEJHH3n9Fqj56XaS2muCCVpsAsGj7cX1/Yr84o5vjdBwaXk6cOCG1tbUSHR3d5Lx6vG/fvrO+RtXFnO356vzZqOGlP/7xj63YapiBKtpVQzXqaNi8MPNUmRzML9FHxqkyOVFcpXtVTpVV6WGg6hq7vlX8vD30wnhqY8PwQB+9PLzahTkq2Ec6hQfodT3UOWaV4FxC/b3lr7/sIytSX5CqXp+Id221VHp4yuyhk+TBWhvbDOCSfHfklN4RXe9l1qPpZyLaoObF0VSvzpk9NarnRQ1LwbWoWpdOEQH6ULssA23lys/e0D0u1Z5e4lNTLfZnnpGJe+/RW150jWaGGS7OJ5sy9e343rFsvnoWDv3TICIiQjw8PCQ3N7fJefU4JibmrK9R51vyfB8fHz02duYBAG3ijOJcr+oq2Xf/b3QNzE8+fV2uf2WtfLAxQ9fIAC2h6vk+35mt708axB/jbR5evL29ZcCAAbJixYrGc6pgVz0eNmzYWV+jzp/5fGX58uXnfD4AGOLMWUX1NS7dZz8vJf9vpg4w01a/L79fsFPuf3+rFP5glhpwPqogvLLGJsnRQZbbKsU0w0ZqSOe2226TgQMH6rVd1FRpNZto6tSp+utTpkyRuLg4XbuiPPTQQzJq1Ch54YUXZPz48fLRRx/J5s2b5Y033nB0UwGg+dQ6Lmcpzg380x/F5u0how+fkDkebnp7iO8zC+Qfk/vpvauAC/l4U4a+/dWgeOrujAovaupzfn6+zJw5UxfdqinPS5cubSzKzcjI0DOQGgwfPlyv7fLkk0/K73//e71InZppxBovAJzKeRagc585UwaIyL+OFcivP9ymFzOc9Pp6eejKbjL9J0lsvolzUutKqbVd1NIOansUnB3bAwCAA6kp/DMX7pL527L04xFJ4fLSjf30LDfgh2Yu2iXvrD8q1/WOlVdu6i+upKgFn9/M5QMAB1JbRvxtUl/526/66On5as+u8S+t1esTAWcqr6qVBfUhl0Ld8yO8AEAb+Fn/DvLv6SP0CtA5RRV6GGnu2sPMRkKjRduzpLiiRjqG+cuILhFGN8epEV4AoI2odV8WTR+p1+5Q20+o3aqnf7hNDy3BtakQ+/b6o/r+rUMTxJ26qPMivABAGw8jvTK5nzx9fYrecO/zHdlywytrZX9usdFNg4HUMKLa2kTt0fbLgR2Mbo7TI7wAQBtT01+njkiUj+8ZKjHBvnIov1Qmzv5WltQvTAbX09DrMqFPnN56AudHeAEAgwxICJPFvx6pZyCpnc7VgnYvfJmmN+WD68grqpAv6oPrrcMSjG6OKRBeAMBAEYE+8vbUwXLXyET9+OWV6XL3u5uluIJVeV3Fh99l6hqoAQntJDUuxOjmmALhBQCcYJf0J69L0dOpvT3d5au9eXoY6VB+idFNg4NVVNfKuxvqhoym0OvSbIQXAHCi6dSf3jNM18EczC+VCbO/lVX78oxuFhxo4bYsOVFSKe1DfGVcr1ijm2MahBcAcCJ94kPl3w+OkIEJ7fSaH3e8vUleXZ3OejAWpGqb/vnNIX3/jpGJ4uXBR3JzcaUAwMlEBfnKB9OGyuTBHUVllueWpsmvP9quhxhgHSv35eketiBfT7lxcEejm2MqhBcAcEKq9mXWz3rJnyam6vVg/vP9cb0qr5qZAmt4o77X5aYhHfX6P2g+wgsAOLFbhibIu3cOkVB/L/n+WKHc8Mq3eudhmNv2zAL57vAp8fJwk6nD62aaofkILwDg5IZ1CZeF9/93X6RfzlkvS3exoJ2ZvbIyXd/e0CdOYkJ8jW6O6RBeAMAEOkUEyPz7R8hlXSOkvLpW7n1vq8xeRSGvGames6/25oravuj+K7oY3RxTIrwAgEmE+HnJW7cPktuHd9KPn1+WJo98TCGvWXtdru/TXrpEBhrdHFMivACAyRa0+8MNPeXZiani4e4mC7cfl5v+uUHyiyuNbhqaQW2+uHR3jri5iUy/Isno5pgW4QUATOjWoQl6W4FgX0/ZmlGgV+RVH4wwR6+LWpCua3SQ0c0xLcILAJjUyK4RsuCBEZIYESBZBeXy89fWyfI9uUY3C+egwuWS+kLrX/+kq9HNMTXCCwCYmKqZWHD/cBnepW5narWp4+tfH6SQ1wk9t3SfXnRwfO9YSY6h1+VSEF4AwORC/b3l7TsG68XO1IfjrC/2yW8/2yGVNRTyOov1B0/KqrR8veDgb69ONro5pkd4AQALUPvi/M/EVHn6+hQ9BfezLcfkljc36k3/YCzVC/aXpfv0fbXlg5r2jktDeAEAi3Bzc5OpIxLlramD9X45m46clgmvUMhrtKW7cuT7zALx8/KQB69khlFrILwAgMWM6hYpC+4fIZ3C/RsLeb/cnWN0s1ySGrp7blmavj/tskS96SYuHeEFACwoKSpQFj4wQkYk1RXy3vPeFlbkNcDctUfk8IlSiQzykWmXdza6OZZBeAEACxfyzps6WKYMS9CFvKzI27Zyiyrk5ZUH9P0nrukuQb5eRjfJMggvAGDxQt5nJqQ2WZH3xjc2SF5RhdFNs7xZS/bqXq/+HUPlp/3ijG6OpRBeAMBFVuR9947Ben+k7ZkFMmH2t3qDQDjGpiOndFBU2wD88YZUcVdTwNBqCC8A4CKGJ0XIogdGSJfIAMkurJBfzFknS3bWrfiK1i3SnTF/p75/46B46dUhxOgmWQ7hBQBciFpjRG0poGYkVVTb5P73t8o/vjpAIW8rmr0yXdLzSiQi0Ed+d013o5tjSYQXAHAxwb5eMvf2QXLXyET9+O9f7ZcHPtgqJZU1RjfN9NSaOq+uPqjvPzOhpy6aRusjvACAC1LFu09elyLP/by3eHm4yZKdOfLT2d/KwfwSo5tmWjW1Nvndv3ZIjc0uY3tGy7WpMUY3ybIILwDgwn41KF4+vmeYRAf7yIG8Er0i7zIWtLsor6xKlx3HCvXqxs9OSNUrHsMxCC8A4OL6d2wnix+8TAYnhumho3ve3SJ/XZYmtTbqYJpr85FT8tKKujVdVHCJCmYlXUcivAAA9Aqw7981RO4YkdjYizB13iY5XVpldNOcXlFFtTz00XZRWU+t5zKRNV0cjvACAGhc0G7m9Snyjxv7iq+Xu6zZny/Xv7KW9WDOQ83S+n8Lduk9pOLD/HSRLhyP8AIAaGJC3zi9sWPHMH85drpcfvbqOnnr28NMpz6Lud8ekf98f1wXQL84qR9bALQRwgsA4Ed6xAbLf6aPlKtToqWq1iZ//M8eufvdLVJQxjBSg3UHT8ifl+zV938/rocMSGhndJNcBuEFAHBWIf5e8vqtA+QP16eIt4e7LN+TK+P+8Y1sOXpKXJ0aJpr+wTZd1KzqXO4Y0cnoJrkUh4WXU6dOyc033yzBwcESGhoqd955p5SUnH/9gNGjR+upZWce9957r6OaCAC4APV7+PYRiTL//uHSKdxfjhdWyK9e3yCzV6W77GykwrJqueOtTXKqtEpS44Jl1s96MS3aKuFFBZfdu3fL8uXLZfHixbJmzRq5++67L/i6adOmSXZ2duPx3HPPOaqJAIBmSo0Lkf88OFJu6NNeh5bnl6XJr15fL0dOlIorqaiulWnvbJa03GKJCvKR128dKL5eHkY3y+U4JLzs3btXli5dKm+++aYMGTJERo4cKS+//LJ89NFHcvz48fO+1t/fX2JiYhoP1XMDADCeKkZVM5Ge+0VvCfTxlC1HT8u1//hG3ttw1CWKeVVoe/ij7fLdkVMS5OMpb98xWOJC/YxulktySHhZv369HioaOHBg47kxY8aIu7u7bNy48byvff/99yUiIkJSU1NlxowZUlZWdt7nV1ZWSlFRUZMDAOAYanjkVwPj5YuHLpMhiWFSXl0rTy7cJbe/tUlyCivEykv/P/bJdlm6O0fX/7wxZaAuaoaFwktOTo5ERUU1Oefp6SlhYWH6a+dy0003yXvvvSerVq3SweXdd9+VW2655bzfa9asWRISEtJ4xMfHt9rPAQA4u/gwf/lw2lB56roU8fZ0l6/358tVf/9a98LYLFYLU11rk4c/3i4Ltx8XT3c3eWlyXxnWJdzoZrm0FoWXJ5544kcFtT889u3bd9GNUTUxY8eOlV69eumamXfeeUcWLFggBw/W7dB5NirkFBYWNh6ZmZkX/f0BAM3n7u4md45MlM8fHCl9OoRIcUWN7oX5xZx1kpZTLFapcXnwg22yeEe23sDy1Zv7yzWpsUY3y+V5tuTJjz32mNx+++3nfU7nzp11rUpeXl6T8zU1NXoGkvpac6l6GSU9PV26dOly1uf4+PjoAwBgjK7RQTL//hHyzvojek+krRkFMv6lb+TuyzvL9J8kib93iz5qnMaJkkq5+53N+udRQ0Wv3dJfruwRbXSz0NLwEhkZqY8LGTZsmBQUFMiWLVtkwIAB+tzKlSvFZrM1BpLm2L59u76NjSXlAoAzUyvMTh2RKNekxsjTi3bLl3ty5dXVB2X+1iz57dhkvRaK6qkxiwO5xXLH25sk81S5hPh5yZxbBjBU5ETc7A4qEb/22mslNzdX5syZI9XV1TJ16lRdwPvBBx/or2dlZcmVV16ph4YGDx6sh4bU18aNGyfh4eGyY8cOeeSRR6RDhw7y9ddfN/v7qoJdVfuihpCYqQQAxli2O0eeXbxHby+gqPVQnhyfIkM7O3cAUB+Jn24+Jk//e7cuRk4I95e5tw+SLpGBRjfN8opa8PntsL48NWto+vTpOqCoWUY///nP5aWXXmr8ugo0aWlpjbOJvL295auvvpIXX3xRSktLdeGtes2TTz7pqCYCABxkbM8YGdUtUt5ed0ReWZkuu7KK5MY3NuhzD43pKv07tnPKxeeeXLRL71WkjEyKkJcm95OwAG+jm4a26nkxCj0vAOBcTpZUyt+/2i8ffpfZuCrv5d0i5dc/SdL7ARm9Oq36GFy0/bj86fM9cqKkSg+BPXZ1N7n38i6mGupypc9vwgsAoE1knCyTV1YdkH9tzWoMMWqW0u0jOsm4XrHi49n2K9Vuyzgtzy1Nk/WHTurHXSID5Llf9GGTRQMQXggvAODUIebV1ekyf1uWVNXY9LmIQG/5+YAOurC3e4xjf3erj72tGaf1cNaqtHx9zsfTXX59ZVeZdllnvW4N2h7hhfACAKYYTvpoU6a8u/6o5BT9d3Xe7jFBuidmdHKkpLYPabWhm7ziClmyI1sPX6m9iRQ1RPSzfnE6uKiF92AcwgvhBQBMtYLtir15snBblqzclydVtXW9MQ09MsO7REjvDiHSNz5UUtoHN3vdmNOlVbIjq1APDakelu8zCxq/5uvlrjeZvH90knSKCHDIz4WWIbwQXgDAlNSMn6W7s3WY+Tb9hJRW1f7oOZFBPhLfzk8iAn0k0NdTArw9pdZul8pqm5RW1kh2YbkcL6yQ/OLKH71WhaCf9+8gE/vF6fVb4DwIL4QXADA9VQ+z+cgp2Xz0tOw4ViDfHys8ayA5n84RAZIaF6IXmPtJ9yiJDvZ1WHthgXVeAAC4FKpwdnhShD4U9bd2YXm1XvU283SZnC6rkpKKGt3b4uHurp/v7+0hMSG+0j7ETzqG+9O7YlGEFwCAKaj1YEL9vfXRq0OI0c2BgZgPBgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATIXwAgAATMVyu0qrLdOVoqIio5sCAACaqeFzu+Fz3KXCS3Fxsb6Nj483uikAAOAiPsdDQkLO+xw3e3MijonYbDY5fvy4BAUFiZubm7hCUlVBLTMzU4KDg41ujlPjWrUM16v5uFbNx7VqPle7Vna7XQeX9u3bi7u7u2v1vKgfuEOHDuJq1BvbFd7crYFr1TJcr+bjWjUf16r5XOlahVygx6UBBbsAAMBUCC8AAMBUCC8m5+PjI08//bS+xflxrVqG69V8XKvm41o1H9fKhQp2AQCAtdHzAgAATIXwAgAATIXwAgAATIXwAgAATIXwYkL/8z//I8OHDxd/f38JDQ1t1mtuv/12veLwmcc111wjVncx10rVsM+cOVNiY2PFz89PxowZIwcOHBCrO3XqlNx88816MSx1re68804pKSk572tGjx79o/fVvffeK1Y0e/Zs6dSpk/j6+sqQIUPku+++O+/zP/30U+nevbt+fq9evWTJkiXiKlpyrebNm/ej95B6nStYs2aNXH/99XpFWfVzL1y48IKvWb16tfTv31/PQEpKStLXzxURXkyoqqpKfvnLX8p9993XotepsJKdnd14fPjhh2J1F3OtnnvuOXnppZdkzpw5snHjRgkICJCxY8dKRUWFWJkKLrt375bly5fL4sWL9S/Wu++++4KvmzZtWpP3lbp+VvPxxx/Lo48+qqetbt26Vfr06aPfE3l5eWd9/rp162Ty5Mk6AG7btk0mTpyoj127donVtfRaKSown/keOnr0qLiC0tJSfX1U2GuOw4cPy/jx4+WKK66Q7du3y8MPPyx33XWXLFu2TFyOmioNc3rrrbfsISEhzXrubbfdZp8wYYLdVTX3WtlsNntMTIz9+eefbzxXUFBg9/HxsX/44Yd2q9qzZ49aMsG+adOmxnNffPGF3c3NzZ6VlXXO140aNcr+0EMP2a1u8ODB9gceeKDxcW1trb19+/b2WbNmnfX5v/rVr+zjx49vcm7IkCH2e+65x251Lb1WLfk9ZmXq39+CBQvO+5zHH3/c3rNnzybnJk2aZB87dqzd1dDz4kJUd2NUVJQkJyfrnoiTJ08a3SSno/6yycnJ0UNFZ+61obq+169fL1alfjY1VDRw4MDGc+oaqL3CVO/T+bz//vsSEREhqampMmPGDCkrKxOr9d5t2bKlyXtCXRf1+FzvCXX+zOcrqvfByu+hi71WihqeTEhI0JsQTpgwQfcA4sdc9X3lEhsz4txDRj/72c8kMTFRDh48KL///e/l2muv1W96Dw8Po5vnNFRwUaKjo5ucV48bvmZF6mdTwfZMnp6eEhYWdt6f+6abbtIfOmrMfseOHfK73/1O0tLSZP78+WIVJ06ckNra2rO+J/bt23fW16hr5mrvoYu9VuqPqblz50rv3r2lsLBQ/vrXv+o6NRVgXHGT3fM51/uqqKhIysvLdY2eq6DnxUk88cQTPypa++Fxrn/8zXHjjTfKDTfcoAsH1di7qmnYtGmT7o0xG0dfKytx9LVSNTHqLz/1vlI1M++8844sWLBAB2SgOYYNGyZTpkyRvn37yqhRo3TwjYyMlNdff93opsGJ0fPiJB577DE9I+h8Onfu3GrfT/23VFd/enq6XHnllWImjrxWMTEx+jY3N1fPNmqgHqtfrmbT3Gulfu4fFlTW1NToGUgN16Q51PCaot5XXbp0EStQ/05U76R6D5xJPT7XtVHnW/J8q7iYa/VDXl5e0q9fP/0eQvPeV8HBwS7V66IQXpyE+ktDHW3l2LFjuublzA9os3DktVLDauoXxIoVKxrDiuqSVXUfLZ3dZaZrpf76LSgo0PUKAwYM0OdWrlwpNputMZA0h5oBoZjxfXUu3t7e+pqo94TqtVTUdVGPp0+ffs7rqb6uZoM0ULO41Hkru5hr9UNq2Gnnzp0ybtw4B7fWfNT754dT7pe7wPvqrIyuGEbLHT161L5t2zb7H//4R3tgYKC+r47i4uLG5yQnJ9vnz5+v76vzv/nNb+zr16+3Hz582P7VV1/Z+/fvb+/atau9oqLCbmUtvVbKX/7yF3toaKh90aJF9h07duhZWomJifby8nK7lV1zzTX2fv362Tdu3Ghfu3atfn9Mnjy58evHjh3T10p9XUlPT7c/88wz9s2bN+v3lbpenTt3tl9++eV2q/noo4/0jLN58+bpmVl33323fo/k5OTor9966632J554ovH53377rd3T09P+17/+1b537177008/bffy8rLv3LnTbnUtvVbq3+ayZcvsBw8etG/ZssV+44032n19fe27d++2W536PdTwO0l9HP/tb3/T99XvLUVdJ3W9Ghw6dMju7+9v/+1vf6vfV7Nnz7Z7eHjYly5danc1hBcTUtOe1Rv9h8eqVasan6MeqymISllZmf3qq6+2R0ZG6l+gCQkJ9mnTpjX+MrGyll6rhunSTz31lD06Olr/Er7yyivtaWlpdqs7efKkDisq5AUHB9unTp3aJOSpgHLmtcvIyNBBJSwsTF+npKQk/Uu1sLDQbkUvv/yyvWPHjnZvb289HXjDhg1Npoyr99qZPvnkE3u3bt3089X01s8//9zuKlpyrR5++OHG56p/c+PGjbNv3brV7grUv6Wz/X5quD7qVl2vH76mb9+++nqpPxbO/N3lStzU/xjd+wMAANBczDYCAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAACmQngBAABiJv8f62dHtzt8NKQAAAAASUVORK5CYII=", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = 0.0\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "ce32e3d1", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "2-element Vector{PyCall.PyObject}:\n", + " PyObject \n", + " PyObject " + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew = newton_step(xguess[end])\n", + "xguess = [xguess xnew]\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "markdown", + "id": "8fe9569e", + "metadata": {}, + "source": [ + "### Wow! Newton actually pushed us to a worse solution with a higher objective value. Why?" + ] + }, + { + "cell_type": "markdown", + "id": "4f5bf8f6", + "metadata": {}, + "source": [ + "# Globalization Strategy 1: Regularization" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "82b98ed7", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-2.0" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "∇2f(0.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7e12451f", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "regularized_newton_step (generic function with 1 method)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function regularized_newton_step(x0)\n", + " β = 1.0\n", + " H = ∇2f(x0)\n", + " while !isposdef(H)\n", + " H = H + β*I\n", + " end\n", + " xn = x0 - H\\∇f(x0)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "02b2106a", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = 0.0\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "7dcde9d4", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "2-element Vector{PyCall.PyObject}:\n", + " PyObject \n", + " PyObject " + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew = regularized_newton_step(xguess[end])\n", + "xguess = [xguess xnew]\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "markdown", + "id": "ffb52534", + "metadata": {}, + "source": [ + "### Ok this is better as we move to right direction of descent however we overshot the minima! We will fix this with Line-Search" + ] + }, + { + "cell_type": "markdown", + "id": "0a5bf49d", + "metadata": {}, + "source": [ + "# Line-Search" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "6ae74c4d", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "backtracking_regularized_newton_step (generic function with 1 method)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function backtracking_regularized_newton_step(x0)\n", + " b = 0.1\n", + " c = 0.5\n", + " β = 1.0\n", + " H = ∇2f(x0)\n", + " while !isposdef(H)\n", + " H = H + β*I\n", + " end\n", + " Δx = -H\\∇f(x0)\n", + " \n", + " α = 1.0\n", + " while f(x0 + α*Δx) > f(x0) + b*α*∇f(x0)*Δx\n", + " α = c*α\n", + " end\n", + " print(α)\n", + " xn = x0 + α*Δx\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "9367632d", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = 0.0\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "a54bd350", + "metadata": { + "vscode": { + "languageId": "plaintext" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "4-element Vector{PyCall.PyObject}:\n", + " PyObject \n", + " PyObject \n", + " PyObject \n", + " PyObject " + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew = backtracking_regularized_newton_step(xguess[end])\n", + "xguess = [xguess xnew]\n", + "plot(x, f(x))\n", + "plot(xguess, f(xguess), \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d5ee59ea", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/class02/part1_root_finding.ipynb b/class02/part1_root_finding.ipynb new file mode 100644 index 0000000..89ea819 --- /dev/null +++ b/class02/part1_root_finding.ipynb @@ -0,0 +1,442 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m new project at `~/Desktop/Summer_2025/Opt-Control-Deza`\n", + "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Desktop/Summer_2025/Opt-Control-Deza/Project.toml`\n", + "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Desktop/Summer_2025/Opt-Control-Deza/Manifest.toml`\n" + ] + } + ], + "source": [ + "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Part 1 — Root Finding & Backward Euler \n", + "## Goal: Solve r(x_{n+1}) = x_n + h f(x_{n+1}) - x_{n+1} = 0\n", + "### • As a fixed point: x_{n+1} = x_n + h f(x_{n+1})\n", + "### • Via Newton: solve ∂r Δx = -r with Jacobian ∂r = ∂/∂x [x_n + h f(x) - x]\n", + "### • Compare convergence of fixed-point iteration vs. Newton (quadratic) " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using ForwardDiff\n", + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pendulum_dynamics" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "pendulum_dynamics(x)\n", + "\n", + "\n", + "Simple undamped pendulum in state-space form x = [θ; θ̇]:\n", + "\n", + "\n", + "θ̇ = v\n", + "v̇ = -(g/ℓ) sin(θ)\n", + "\n", + "\n", + "Returns the time derivative ẋ = [θ̇; v̇].\n", + "\"\"\"\n", + "function pendulum_dynamics(x)\n", + " l = 1.0\n", + " g = 9.81\n", + " \n", + " θ = x[1]\n", + " θ̇ = x[2]\n", + " \n", + " θ̈ = -(g/l)*sin(θ)\n", + " \n", + " return [θ̇; θ̈]\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "backward_euler_step_fixed_point (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "backward_euler_step_fixed_point(fun, x0, h; tol=1e-8, maxiter=10_000)\n", + "\n", + "\n", + "Implicit step via **fixed-point iteration** on\n", + "x = x0 + h * fun(x).\n", + "\n", + "\n", + "Converges only if the fixed point is stable and the initial guess lies in its\n", + "basin of attraction. Returns `(x_next, errors)`, where `errors[k] = ‖r(x_k)‖` and\n", + "r(x) = x0 + h * fun(x) - x.\n", + "\"\"\"\n", + "\n", + "function backward_euler_step_fixed_point(fun, x0, h)\n", + " par\n", + " e = [norm(x0 + h.*fun(xn) - xn)]\n", + " while e[end] > 1e-8\n", + " xn = x0 + h.*fun(xn)\n", + " e = [e; norm(x0 + h.*fun(xn) - xn)]\n", + " end\n", + " \n", + " return xn, e\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "backward_euler_step_newton" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "backward_euler_step_newton(fun, x0, h; tol=1e-8, maxiter=100)\n", + "\n", + "\n", + "Implicit step via **Newton's method** on the residual\n", + "r(x) = x0 + h * fun(x) - x.\n", + "\n", + "\n", + "Uses ForwardDiff.jacobian to obtain ∂r/∂x at the current iterate. Quadratic\n", + "convergence near the root; typically many fewer iterations than fixed-point.\n", + "Returns `(x_next, errors)`.\n", + "\"\"\"\n", + "function backward_euler_step_newton(fun, x0, h)\n", + " xn = x0\n", + " r = x0 + h.*fun(xn) - xn\n", + " e = [norm(r)]\n", + " while e[end] > 1e-8\n", + " ∂r = ForwardDiff.jacobian(x -> x0 + h.*fun(x) - x, xn)\n", + " xn = xn - ∂r\\r\n", + " r = x0 + h.*fun(xn) - xn\n", + " e = [e; norm(r)]\n", + " end\n", + " \n", + " return xn, e\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "backward_euler_fixed_point" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "backward_euler_fixed_point(fun, x0, Tf, h)\n", + "\n", + "\n", + "Integrate using backward Euler where each implicit step is solved by fixed-point\n", + "iteration. Returns `(x_hist, t_hist)`.\n", + "\"\"\"\n", + "function backward_euler_fixed_point(fun, x0, Tf, h)\n", + " t = Array(range(0,Tf,step=h))\n", + " \n", + " x_hist = zeros(length(x0),length(t))\n", + " x_hist[:,1] .= x0\n", + " \n", + " for k = 1:(length(t)-1)\n", + " x_hist[:,k+1], e = backward_euler_step_fixed_point(fun, x_hist[:,k], h)\n", + " end\n", + " \n", + " return x_hist, t\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "backward_euler_newton" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "backward_euler_newton(fun, x0, Tf, h)\n", + "\n", + "\n", + "Integrate using backward Euler where each implicit step is solved with Newton.\n", + "Returns `(x_hist, t_hist)`.\n", + "\"\"\"\n", + "function backward_euler_newton(fun, x0, Tf, h)\n", + " t = Array(range(0,Tf,step=h))\n", + " \n", + " x_hist = zeros(length(x0),length(t))\n", + " x_hist[:,1] .= x0\n", + " \n", + " for k = 1:(length(t)-1)\n", + " x_hist[:,k+1], e = backward_euler_step_newton(fun, x_hist[:,k], h)\n", + " end\n", + " \n", + " return x_hist, t\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "PyObject " + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# --- Demo: compare fixed-point vs Newton for the pendulum ---\n", + "x0 = [0.1; 0.0] # small-angle start (near-stable regime)\n", + "Tf = 10.0\n", + "h = 0.01\n", + "\n", + "\n", + "x_hist1, t_hist1 = backward_euler_fixed_point(pendulum_dynamics, x0, Tf, h)\n", + "x_hist2, t_hist2 = backward_euler_newton(pendulum_dynamics, x0, Tf, h)\n", + "\n", + "\n", + "figure()\n", + "plot(t_hist1, x_hist1[1, :], label=\"θ (fixed-point)\")\n", + "plot(t_hist2, x_hist2[1, :], label=\"θ (Newton)\")\n", + "xlabel(\"time t\"); ylabel(\"angle θ\"); title(\"Backward Euler (implicit) with two inner solvers\"); grid(true); legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.3007510554383426e-6" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Numerical check that trajectories agree (up to tolerance/roundoff)\n", + "maximum(abs.(x_hist1 .- x_hist2))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "([0.09107763165756541, -0.08922368342434606], [0.09793658173053843, 3.7830087232931797e-6, 5.2874553670659e-15])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# --- Single-step convergence histories ---\n", + "(xn_fp, e_fp) = backward_euler_step_fixed_point(pendulum_dynamics, x0, 0.1)\n", + "(xn_nt, e_nt) = backward_euler_step_newton(pendulum_dynamics, x0, 0.1)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "14-element Vector{Float64}:\n", + " 0.09793658173053843\n", + " 0.009793658173053846\n", + " 0.009564124766684667\n", + " 0.0009564124766684723\n", + " 0.0009343853483241293\n", + " 9.343853483241571e-5\n", + " 9.128296581455142e-5\n", + " 9.128296581450979e-6\n", + " 8.917746787032166e-6\n", + " 8.917746786990532e-7\n", + " 8.712050176828967e-7\n", + " 8.712050177106523e-8\n", + " 8.511098474606182e-8\n", + " 8.511098478769519e-9" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "e_fp" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " 0.09793658173053843\n", + " 3.7830087232931797e-6\n", + " 5.2874553670659e-15" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "e_nt" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ERK7OZDKpmddlUErGyXgzYpCUSxIg2WsRTSIiIipYsmRPVosoCwZJuSQtSOZKlhXi7T1HjayGbV7igVgnmWG9WGOdWGOd2MZ6cc06iYqKUo0c5vN4Vhgk5ZK5i00CpPwIkmTFbnleZ/2Q5hTrxDbWizXWiTXWiW2sF9euE0M2UmWYuE1ERERkA4MkIiIiIhsYJBERERHZwJwkIqJ8ni4kISFB8zwTd3d3xMXFITk5WdOy6AnrxXnrxNPT867D+7ODQRIRUT6R4CgsLEwFSlrPCyOLE8toXM7rdgfrxXnrxGg0okKFCipYygsGSURE+XSyuXjxItzc3NRwY3v8qs0tCdKio6NRuHBhTcuhN6wX56yTlNuTPcv/v7Jly+Yp2GOQRESUD5KSkhAbG6tm9ZUh1Xro8vP29nbYE19+YL1Yc5Y6KV68uAqU5P9hXqYycNwaICLSMXM+R16b+4ko58z/7/KaV+XSQVLPnj1RrFgx9OnTR+uiEJGTcuS8DiJX/3/n0kHS8OHD8cMPP2hdDCIiItIhlw6S2rVrl621W4iIXCnh/LnnnkNAQID6Nb537171Xfnyyy/n63HHjh2L+vXrI7/Nnj0bRYsWhaPITt2XL18ekyZNsutxBwwYgIceegiuTrdB0vr169G9e3eV9Cj/URcvXmy1z7Rp09SHQxLMmjVrhu3bt8MZXD5/CnGXDqtrIqKCtHLlShVILFu2TI0Oql27NhYuXIj3338fzqBfv344duxYjh5TEEFiZpyp7h2RboOkmJgY1KtXTwVCtsyfPx8jRozAmDFjsHv3brVv586dcfny5bR95FeJ/AfPeJGMd73a/tsklPyuGfpdnKCu5T4RUUE5efIkSpUqhXvuuUfNlyMTC0qrkrO0uvv4+KBEiRIFcix7TCLqTHWf3cks9US3QVKXLl3wwQcfqORqWyZOnIhBgwapJsGaNWtixowZapjtrFmz0vaRZuKDBw9aXaR1Kqfi4+MRFRWV7mJ+Q+11OX/6KBrvHws3g0k9t1w33D9ObbfncRz1Yu/6dpYL60W/dSJdVzKkOq+X89djsOn4FXWdm8dLOcTdytO/f38MHToUZ8+eVS340lIv26UlRXI45fahQ4fUd+1PP/2U9riff/5ZBR/y/Sr3r127hmeeeUYNw5bV5O+9917s2bMn3bEmTJiA4OBgFQAMHDgQt27dUmXMqnxSjpdeekld/P39ERQUhHfeeUeNYDLvc/XqVTz55JNqUI6U8/7778fRo0fT/i7nCOluM9fLRx99hIYNG+L7779Xr1eeV1qbIiMj0+pk3bp1mDx5sqoTuZw6dcpm+eTx7733njq+vG45R8l26Rlp3bq1qiOZM0vq+ObNm2mPk8aAKlWqqF4RqZPevXune83mupfLpUuX8MADD6jnkskSf/zxx3TvrZRNyiiNB+bHyPsh2/7++291Xz6bUufyeHmeatWqqe46y8/K3T4vs27X44oVK1CjRg01r5I0VJw/fz5tHxl+P27cOJQpUwZeXl6q4eKPP/5I+7u5rPPmzUPbtm3V65fXI3Xeo0cPfPjhh6o+5DjyPBJ0vvbaaypwlOf89ttv7/q5z+o7wmnnSZKK2rVrF0aNGpW2TeZz6NChA7Zs2ZIvx5T/0PImZfTXX3/ZbQ4U6WLrdztAMnM3pGDDysXwKVXdLsdwdKtWrdK6CLrEetFfnUgLjLTEyMR88p0lX9hxiTmfeXvpgcv4ePUppJgAowF4s0NFPFgnZy0h3h5GdTKSE3NW5AQvJx/pbpMTqkyEKT8I5WQnr0Fuy49M2U8CFWnBl+/ewYMHq5wieazsIyd5OeH98ssvKliQ55Pv5507d6rgZdGiRer79JNPPkHz5s1Vz8D06dNRrly5tB+gtkg5ZLDNE088gdWrV6vA65VXXlHBmJxYhQQocvKdM2eOCsDkOF27dsXWrVvVfDmy3Ia8F5bHkdaz3377DXPnzsWNGzdUACGv8d1331XXhw8fVj/GzeccCaRslVNOzJ9++ineeOMNFViJffv2qeO//fbbKhCJiIhQf3/hhRdUcCSvQYIg+aHftGlTdXw5j5mf37Luza9PAqWlS5eq1/Pmm2+qHhR5XbKPfN7MvTHmx5jfd5m3S7ZJkCB1JoGOBBzbtm1T9Sivy9wwIfskJSVl+n7I8eT5/ve//+HLL79Un4Pnn39edUvOnDlT7SPbP/vsM3z++eeoW7euCqwlz0leX6VKldLKOnLkSNUoMmXKFBVMyXu7du1a1eIn3b5SPgksN2zYgBYtWqj/2/IZks+dfH5Kly5tVT6pMwm8JUCV12FJyu3UQZJ8yOSXg0SYluT+kSNHsv088p9WPsDyYZL/3AsWLFBvgC3yn0O698zkgyO/CDp16qS+BOzh8vnqSP7uo7SWJJFkMmKLoSbeaXcfivrmfkIsRyf/YeU/RseOHfM0MZizYb3ot07kJCJLO8gvbAkYYhOS0ODjvAVuEihNWHVKXXLiwJgOSI6/pYKGrIZGy3eZtM5IvUnLhmXAJ/POmL/r5LtQTmISKMn2Jk2aqF/48twbN25UrRhyIpcTnmjQoIFqcfjzzz9VUricRCUQkceLRo0aqcdJnWX1fSrlkO/dL774Qh1LHicBzldffaVOosePH1fHkZOpdBcKaaWQ4EuCvr59+6r3Qh4rxzG3mkhwIy0Y5m4tCUTkOWQfucgPYQkgLOvEFgkUpNXsrbfeStsmrUmPPfaYCmbMpk6divbt26t6kJavQoUKqbKZj9+qVSubdS+5VBJASMAndS6+++471KpVS70u2Uc+b0Ke01yX5mVx5HWYt8kPf7M6deqoc6EEJE899ZQKquQz4O7unun7IceT/2tff/21CniEvAeSP2V+jASB8rqlx8f8PkuAJC1A8h6ayyoB2uOPP5723HJsCd4kcJY6lcfJ/hL4mBsrJOiSoFPKLS1ZGclnSVrJ2rRpo8pqKatA3CmCJHuRD1t2yX928394S/Jm2uuLuHT5athed6zqcjMaTJD/v+8kPYMlYUbs+HILJj/aAE3KB8CV2bO+nQnrRX91Ij/k5GQsX/Lmi1bMgZG5PNnZN+N+GR8rJ+eqVauqbf/++69qdRIHDhxQLQTSUmFJftXLOnayv7TMSEuK5fPJD1QJvGSbBCiScmEmQZD5JCotB+ZjCQmGJP1CAh7pVpMTuzyX+bmlHNKdJH+zfB/k2hw8mLvZzKS1TFpnLMuXnboTErxY7rd//351kVaqjN1YZ86cUV1UEsRVrlxZdQ3KRVpzLHsozMc2vz7LY0gLl3RHWX7WzK/P8nbGbRLASEuSdK3KeyMBiHSHWQbRhixes2yXMloGjpb1JoGI5P9KwGf5HC1btlSBjWVZMtaZHFcCP3mtlo0gklNs+VoCAwNVo4mtMso2eR5b3wM5+V5wyCBJfunIf5Lw8PB02+W+NG87sqa9X0Z4xaoIXvIo4OaJJ55+BVt/PYbTV2PR76steLlDVbzUvjLcpN2diByGj4cbDr3XOUePuRQZhw4T16kWJDP5r796RFuU9E//6zgrXm4G3IyDXZlb4eVkJKPgJNlbSIAkt//55x+rx2R36H3jxo1VTqlZxl4De8t40pSTa24XJZYWHEtSH9INNWzYMKt9ZV0xaSWSljepL0nfGD16tOq63LFjR66mKjAHDJa5RRlzcCSHTFr+pCtMAkppwZKuT+nWymu9mSyOm9s6y+y57fk+OXzidlbkQyXNb2vWrEnbJhUl9zPrLnMkAbU6INqzBAwpCah9axeWDWuNng1Kqy/KiauO4fFvtqovTyJyHPKF7uvpnqNLxeKFMaFXHbjd/nUv13Jftufkeew967ckAj/99NMqz0aupZXHnHgtSdDS1SatANI6YnmRH7hCukcynpClC8lMukksH2c5usvW46Q1Q344y/NK/onlPtKdJS0w0uKSl3NObpe3kPqQZPeMdSEX89IZUleS/iH5PdLqdPr0adU9mFH16tXV65OcXDN5bZLHZGZuwZPA1cwy4BSbNm1SLXAvvvii6gqVski3pT35+fmpliU5VsZj5+W9KGi6bUmS6PvEiRNp96WZVt5o6aeU6Fv6xCVRT35xSLKb9E3Krxpz36dDMxhwyb8hKl9ZCRxZjsI1H8Tn/eqjVeUgvLvkILaeuoYuk9fjkz710KFm/v7CIiJt9WtSFm2qFsfpiFiUD/JFKX8frYukusokN0hGlsnIXznRSsuEdOHIyV5+rEqCrpz0pUtOul2WL1+uupHkO1sSlSW4ktvS/SJJ1tJlV7FixbseW7qH5PtfWmekBUbye6RFREiwJKOiJA9IuugkuJKkYEnsle25Jd1xEnhJ8CJ5NHIeym73qeTkSBfhkCFD8Oyzz6pWEwmaJG9O8mwkD0gSzSV3RpLazaO/pIswI9km3XHy2iVfR4IrSZSWoNJMbsvxZNSejF6T7i95nyxJPUkCvOSImUfIScuV3Lan119/XU3TIzlL0pUnXbRyHpf321HotiVJRkHIfzy5CPlPIbelKVLIEE0ZRSD3pfKl4mUStPxuli0ol4o2TL1xbCWQnJqZ37tRGSwb2gq1QvxwPTYRz/6wE2OX/ou4xLwt4EdE+iaBUYtKgboIkOTkKidyObHKSVpO+jJqSZKQJWlaWq3k73LSlx+tEiQ98sgjKv/G/P0s398yckxGeUmvgPxNRiplhyQWS6uV/DiWxG8JuCQZ3ExOxPKcMkxegjXp/pHy5CU/TQJAaamSFhBpqZFALbskwVhGuknStUwDYD6PmaeikS41mTBSEr6lJUxGuUmyueTk2CKvTx4rQ+Z79eqlXnvGeZ8k10hanKQeJIiSkWOWJMiSx8r7IBMxS2ubtCrZ27Bhw9S5+9VXX1XJ4XKOllF5d0uA1xODKTcdiKSS0iTRT+bSsNfoNsv+4xXLf0f3Y6/BEHsV6P87UKFN2t/jk5Lx8YqjmLUpTN2vWcoPUx9rgErFU0cKOCOpE/mik6G0TFC+g/Wi3zqR0TXSAi6/zjOOrilo0jIh31nyXaVlAnleyZxB8qPYXktwOEu92JOz1ElcFv//cnL+dtwacHImgxtMlTul3jnyR7q/ebm7YXT3mpj1dGMEFPLEoYtR6D51IxbsPJerpDkiIiKyxiBJx1Kq3h4Ce3S5DFWw+vu91YOxYnhrtKgYiNiEZLz+634M/3kvbsbpa1p3IiIiR8QgScdMFdsB7j7AjbNA+EGb+wT7eeOnZ5vh9c7V1LQAS/ddQLcpG7Hv3J3RDkREzkCGydt7tXuirDBI0jMPX6DSvTa73CxJcCRzJ/3yfHOULuqDs9di0Xv6Zny17iRSLCdYISIiomxjkKR31bumXh9ZdtddG5ULwB/DW6NrnZJISjFhwoojeHr2Dly5GZ//5SQiInIyDJL0rur9gMEIXNoP3Dh31939fTww7bGGGN+zDrzcjVh/7Aq6TN6gromIiCj7GCTpXaEgILR56u2jmXe5WZJ5Sh5rVha/D22FqsGFEREdj6dmbceEFYeRkJS/U7gTERE5CwZJjqB6t9TrI8tz9LCqwUWwdEgrPN6srLr/1bpT6PvVFpy9GpsfpSQiInIqDJIcKS/p9Ebg1vUcPdTbww0f9qyD6Y83hJ+3uxr11m3KBjUKjoiIiDLHIMkRBFQEitcATMnA8VW5eooudUqppO7G5YrhZnwShs3bgzd+3YfYhNQlT4iIKG/TE0iqg+VisxnNnj1bLUNiT7KenBw34yK2ZB8Mkhyuy+3uo9wyU6aYL35+rjmG3VtZ1tDFLzv/wwNTN+LfC5H2KycROTRZeFZOurJAqqXFixer7fll7NixaskRR3XPPffg4sWLarkLch4Mkhyty+3EGiAp90P63d2MGNGpGuY82wzBfl44dSUGPadtxuxNYVzShIgUWevq448/xvXrOeved1TJyclqzbK88PT0RMmSJfM1kNSThIQEuAIGSY6iVAOgSAiQEA2Erc/z091TKQgrhrfBfdVLICE5BWN/P4RBP+zC9RjX+OATOZTI86n/7+W6AHTo0EGd8CdMmJDlfhs3blQr2/v4+CA0NFSt+h4TE6P+9sUXX6B27dpWLVGyyr3lcd555x3VDTVu3Djs27dP7SMX2SbOnj2LHj16oHDhwmox0ocffhjh4eFWLVA//vgjypcvr1pyHnnkEdy8efOu3V6yIn3z5s1V+eU48fHxeO2111C6dGkUKlQIzZo1U91oZmfOnEH37t1RrFgx9fdatWqpxZQz626T45QtWxa+vr7o2bMnrl69atVq99BDD6Xb9vLLL6uFfM1WrlyJVq1aqfIGBgbigQcewMmTJ5ETUi/jx4/HwIEDUaRIEVWmr7/+Ot0+Bw4cwL333qteV8WKFfH8888jOjraqqwffvghQkJCUK1atbSuvl9++SXtc9CkSRMcO3YMO3bsQOPGjdX71qVLF1y54pjT0DBIchSyGnO1LnnucrMki+N+078xxnSvCU83I1YfDldzKm09lf4/MhHZgbTUJsTk/LJ9JjCpNvB999RruZ/T58hhK7Gbm5s6qU6dOhX//fefzX3kRH3//fejd+/e2L9/P+bPn6+CpiFDhqi/t23bFocOHUo7Oa5btw5BQUFpQUdiYiK2bNmiAoJ+/frh1VdfVUGHdFnJRbZJ644ESNeuXVOPX7VqFU6dOqX+lrEsEoQtW7ZMXWTfjN2FGcXGxuKTTz7B5MmTVYBQokQJVXYp088//6xeU9++fdVrPH78uHrMSy+9pAKp9evXq8dIa5sEAbZs27YNzzzzjHpOyRdq3749PvjgA+SUBJ0jRozAzp07sWbNGhiNRhVw5bTl67PPPlNBy549e/Diiy9i8ODBOHr0aNoxOnfurII/KbcEd3KsIbffSzPZJo+R90Hq2WzMmDEq2N29ezfc3d3x2GOP4Y033lB1u2HDBpw4cQKjR4+GI3LXugCUw7yknd8CR1cA3T5PDZzySH4FDGhZAU3KB6hk7lMRMXhs5lYMubcK+jYqjXPXb6FCUCGU8vexy0sgclmJscD4kLw9hykF+OO11EtOjLQd6GRFTsTSQiMnwG+//dbq79LK9Pjjj6uWD1GlShVMmTJFBUfTp09XrUgBAQEqYOnTp48KjiQQkhOn2L59uwqUJJdHWiAk2JATrLRgmcnJWIKRsLAw1VIlfvjhBxVMSUuFtFoICRjkxC6tJOLJJ59UJ3Rp9ciMHFtauypUqKBaqCQY/O6771SLkrSUCGlVkpYc2S5Bo/xNgsI6deqov0uLS2bkdUqAJcGCqFq1KjZv3qyeLyfkeJZmzZqF4sWLqwDUsqXubrp27aqCI/Hmm2/i888/x9q1a1WL0Ny5cxEXF6fqVt4LaWmS97JHjx4qEAwODlaPk1amb775RnUtCmlJMteTBFli+PDhePTRR1X9t2zZUm2TYNHcMuho2JLkSMq3Brz8gOhw4Pwuuz517dL+avLJPo3KQJZ7m7LmOFr/7x88NnMbWn70N+bvOAstXYyMw/FIg7omooIhJ8jvv/8ehw8ftvqbdI3JiU+CG/NFTpQSsEhQIz/A2rRpo4Ij6YKSk7qcpKUl5siRIyp4kiBHuqIyI8eV4MgcIImaNWuqrifLMkl3kjlAEqVKlcLly5ezfG1yoq9bt27afQnGJDdJghnL1yTlNHdvSXeitAbJyV+CR2ltyqrs0l1nqUWLFsgpacWSoEMCMgnm5LUKCdhywvK1ynsjwai5jqSs9erVU0GQmbzGlJSUtNYmIcGhOUDK7LnNAZU5kDRvu9v7oVdsSXIk7p5AlY7Awd+Ao8uB0NRfUfZSyMsdn/athzql/TBm6aG07RI0vfnbAfy45Qy8PNxgNKT+J5Nro7qWHALz7dRry7+b/5bVPtIolu4xt/8jy+3j4Tex8UQETHDDl4fXY0KvOujXJHWCTCKHWrD6rRzOTxZ1AZjWNLUFyczgBry0DfDLQauUmzcQl3mOTmYkyJHAZ9SoUSonxZLkq0jeigQOGUlLhJCuNMl9kS6XBg0aqJO8OXCS4ENanezBw8Mj3X357rhbd5S0mFgmWcvrkW7GXbt2qWtL5i61Z599VtXH8uXL8ddff6nWNOnGGjp0aK7KLV1nGQfMSAuXJcmBKleuHGbOnKlauOR1SQtSThOnc1NHGVkGUZk9t7lOM27La2K8VhgkOZpqXVODJJl9u8PYfDlEleA7v8gsHbwQBa1JwDZq4QG0qVqcXYDkWOTk4Wn7JJOpoCpA98nA7y+nzpMmAVL3SanbcyIPJyjJ7ZFuN+mWsdSwYUPVOlS5cuVMHytBkHTHLViwIC0ZWa5Xr16NTZs2qe43M2mhkJYcSzVq1MC5c+fUxdyaJMeUlilpUbInCeLk+NLiIUnImZFyvPDCC+oiwaMEL7aCJCm75PdY2rp1a7r70m128ODBdNskf8kcYEiit7TkyDHMZZK8L3uTskqroOQmSfAo5P0xGo1W77urYZDkaKQlyegBRBwDIo7n/MsyGyQHSVp0JCAxk/sTetaBv6+n+uUjf0tR1yaVE5p6O/XalLbtzv07+0sOaerj7vxdvsNNkMNl3OfctVtWs4PL33/aegavd65u99dOpDsNnwIq3QdcO5U6sax/6QI9vHSbSO6R5KhYkrwWGRkmyb3SwiKtDBLASB6R5PqYu2EkGVhyXsyJvhIkSQ6LtC6Yc1aEdCNJN50ECWXKlFHdZzL6zXz8SZMmISkpSXXZSfAlScj2JN1scpynnnpKtQ5J0CRJ55JbI6+jW7duKuCTkVqyr0yPIDk9EmDYIi1s8vo+/fRTldvz559/WuUjyWgySR6XXCDpivvpp59U0CTHFlJ3MqJNWuOkC1G62EaOHAl7k9ct3Yf9+/dXCdYyik9e65NPPpnWfeaqGCQ5Gm9/oEJr4OTfqa1JrVKTJu1JWmikS+uthQeRbDLBzWDA+F61Neniuhh5C8v2X0gXsIlpa0+q/KT3etRGYS9+jMnJSWBUwMGRpffee0+NXrMkgYN0mb399tuqlUN+2FSqVCndyDMJhORv0j0lw9jNj5NuN2mhsOy+kQTlhQsXqlFg0lIkydLSxbdkyRLVUiPddNKyIcnQMuouP8gxJedIWrjOnz+vRuNJICjD7oW0NMkIN0nyltcgZZEEaFvkcdICJMGHBB7m6Q7ef//9tH2k6+7dd99Vyd2SOC1D9CVIk/woIa9XRtpJwCVdbFJnEqxaThFgD5IXJkGcJF1LHpW0Jsn78Xkmr82VGEycQTBXoqKi1HwckZGR6j+LPUmftMy9IaMRMvYjKzIEWEa3hDYDnvkL+RmgnI6IRfkgX027tiRpXLrYJFCSFq37agRjzeFwdV9avaY80gB1yrjmLLd3/ay4IL3UiZz0pGVERk/J5IxaknwQ+c6S7yo58VIq1ovz1klcFv//cnL+dtwacPW8JHFuOxCdfyMGJDBqUSlQ89wfacH659U2GFIzWV3PfKox5j/fAiH+3giLiEGv6ZvwzYZTnDGciIjsikGSI5Jm9xDpszalzpnkAkr5e6OKv0ldC5nXSRbs7VwrGInJJnyw/DAGzt6Bq9G5X7KFiIjIEoMkR1/w9mjqlPiuqKivJ2Y80QjvP1Qbnu5GrD16Rc0YvvlEhNZFIyIiJ8AgyVFVux0knVwLxN9ZX8fVSGLok83LYemQlqhcojAu34zH499uwyd/HkFismPOy0FERPrAIMlRlagBFKsAJMenjnRzcdVL+uH3Ia3waNNQNaWAjH7r99UWnLsWq3XRyMUxV47Icf/fMUhy5InpzF1uMhUAwcfTDRN61cW0xxqiiLc7dp+9ga5TNmD5/otaF41ckHnW5pzOjExEeWf+f5dx9vSc4gQzjkyCpC1fAMdWAslJgBvfTtGtbinULeOP4T/vUYHSS3N3Y+OJshj9QE0VSBEVBFmsVeafkQkJZSoCLYdTy7BuOWnIsGhHHtZtb6wX56yTlJQU9f9O/v/J/8O84FnVkck8Sb6BQOxV4OxmoEIbrUukG6EBvmqagEmrj+HLf05i3vaz2Hn6GqY+1kB1zREVRL6czJIsc7XIDMZadz3cunXLar0yV8d6cd46MRqNag3BvL4GBkmOzOgGVO0C7P0JOPIHg6QMPNyMaumSeyoF4ZX5e3H8cjR6fLEJ7zxQE080y/t/HqK7kfXIqlSponmXm0ywuX79ejVrNScdvYP14rx14unpaZeWMAZJjq5619tB0nLg/gmpuUqUTsvKQVgxvDVeW7BPTRPw7uKD2HQ8Ah/1rqOmESDKT/JFrfWM25KXIeueSTkc+cRnb6wXa6yT9Byzw5HuqNgecPcBIs8C4elXk6Y7Agt74dv+TfBOtxrwcDNg5b+X0HXyBuw4fU3rohERkU4xSHJ0nr5ApXtTb3OUW5aMRgOebV0RCwe3RPlAX1yIjFPTBExZcxzJGVfQJSIil8cgyVm63ASDpGyRxXCXDWuNXg1Kq0VyJ646hse/2YpLkXFaF42IiHSEQZIzqHo/YDACl/YDN85pXRqHUNjLHRP71cfEh+uhkKcbtp66hvsnr8eqQ+FaF42IiHSCQZIzKBQEhDaHq6/llhu9GpZRrUq1S/vhRmwiBv2wE2OX/ou4xGSti0ZERBpz2SDpxo0baNy4MerXr4/atWtj5syZcGicfTvXKgQVwm+D78GzrSqo+7M3n0avLzfj5BXXXROPiIhcOEgqUqSImgti79692LZtG8aPH4+rV6/C4fOSTm8Ebl3XujQOx8vdTc2f9N3TTRBYyBOHLkbhgSkb8cvOc1x7i4jIRRldeS4ImbJcxMfHqxOhQ58MAyoCJWoCpmTg+CqtS+Ow2lcvoeZUalk5ELcSk/HGr/sx/Oe9uBmXqHXRiIiogOk2SJJWnu7duyMkJETNjLx48WKrfaZNm4by5curSa+aNWuG7du357jLrV69eihTpgxef/11BAUFwaFVM49yW6Z1SRxaCT9v/DCwGV7vXA1uRgOW7ruAblM2Yu+5G1oXjYiICpBug6SYmBgVwEggZMv8+fMxYsQIjBkzBrt371b7du7cGZcvX07bx5xvlPFy4cIF9feiRYti3759am2luXPnIjw83Dnykk6sARI5nD0vJDh6qX1l/PJ8C5Qu6oOz12LRZ/pmfLXuJM5fj8XmkxG4GHlL62LiYmQcjkca1DUREdmXbpcl6dKli7pkZuLEiRg0aBAGDBig7s+YMQPLly/HrFmzMHLkSLVN8o2yIzg4WAVZGzZsQJ8+fWzuI11ycjGLiopKW+dGLvZkfr4cP2/x2nAvUgqGmxeRdOJvmCp3hLPIdZ3kUd2Qwlj6YnO8s+QQVvwbjgkrjqiLkBVgXmxbEZ1rBsNoSL0vrZ5GdYG6lm3m+wYb942Z3JfFZdLdv/13Swt2/afKlWJyw5eH1+ODHjXRt1EZuDqtPit6xjqxjfXimnWSmIPXZjA5QCKOnBwWLVqEhx56SN2XxSIln+jXX39N2yb69++vutCWLFly1+eUViN5DkngjoyMRMuWLTFv3jzUqVPH5v5jx47FuHHjrLZLC5Q5t0kP6p6bjQoRf+N0YHvsK5saQFLeyf+SNRcM+P2sNL5qsz6eAabbwZMUCEidpMCQ7u9jGyajqJcmxSMicgixsbF47LHH1Lnfz8/PMVuSshIREYHk5GTVAmRJ7h85kvor/27OnDmD5557Li1he+jQoZkGSGLUqFGqe8+yJSk0NBSdOnW6ayXnJspdtWoVOnbsmOMFBg2nfIB5f6Nc3L8o3eX2JJNOIC91Yi+Bp67h9+92Wm0v6uMBdzcDUtRnCepaZvK2vJ/xOjeroEiIpB5myvzvleo3R7MKAXBlevis6A3rxDbWi2vWSdTtnqDscMggyR6aNm2a7e444eXlpS4ZyYcovz5IuXruSu0ALz8YYi7DI3w/ENoEziQ/6/tuKpf0U91flgGOm8GAFS+3Ril/nxw/n8kimDIHUHeCqNS/ZbbPpchb6DV9s1WwdfZ6HFpVdc4vNkf6rOgV68Q21otr1YlHDl6XQzYzyCg0GcKfMdFa7pcsWRIuzd0TqHI7F+koJ5a0JwmEJvSqowIjIdfje9XOVYBk7kaWBHEPN6Oap8nbww0+nm4o5OWOIt4e8PfxQFFfTwQU8kRQYS+UKOKNYD9vlPT3Rv2yxVRZJGiz9Naig3hr0QHOGE5EZAcOGSR5enqiUaNGWLNmTdq2lJQUdb9Fixaalk1fUwEwSLK3fk3KYuPI9pg3qLm6lvtaluWfV9tgSM1k/P1KK7zQtpLaPnfbWTz4xUYcC7+pWdmIiJyBboOk6Oho1R1m7hKTYfpy++zZs+q+5AfJUiLff/89Dh8+jMGDB6tpA8yj3VyatCQZPYCIY0DEca1L43Sk5ahFpcBctyDZtyzeqOJvQmiAL0Z2qY4fn2mqWp2OhUej+9SNmLPtjGNPkkpEpCHdBkk7d+5EgwYN1MUcFMnt0aNHq/v9+vXDp59+qu7LfEgSQK1cudIqmdslefsDFVqn3mZrkktpXaW4mjG8TdXiiE9KwduLDuLFObsRGeu8w3mJiFwuSGrXrl3ayDPLy+zZs9P2GTJkiBqlJvMXyfprMus2ZZhY8ugfWpeECljxIl6Y/XQTvN21BtyNBqw4eAldp2zArjPXtC4aEZFD0W2QRHbKSzq3HYi+Mws5uQaj0YBBbSrit8H3oFygL87fuIWHv9qKL/4+juTczD9AROSCGCQ5K78QIES6Kk3A0RVal4Y0Ui+0KJYNbYUe9UNUcPTpX8fwxDfbEB7FZUyIiO6GQZIrdLkxL8mlyXQCk/rVx6d968HX0w1bTl3F/ZPWY81hB1+rkIgonzFIcmbVbgdJp/4B4qO1Lg1pSOZk6tOoDH4f2gq1QvxwPTYRz3y/E+N+/xfxSZxTiYjIFgZJzqxEDaBYBSA5Hjj5t9alIR2oVLwwFr54Dwa0LK/uf7fpNHp9uRmnrjCIJiLKiEGSM5OZodnlRhnI7N5jutfCt/0bo5ivB/69EIUHpm7Er7v+45xKREQWGCQ5O3OQdGwlkJykdWlIR+6rEYwVw9ugecUAxCYk47UF+/DK/L2IjufnhIhIMEhydqHNAN9AIO4GcHaz1qUhnZF14OY82xyvdaqq1pFbvPcCuk3ZgP3/3dC6aEREmmOQ5OyMbkDVLqm3j3BiSbImwdGQe6tg/nPNUbqoD85cjUXv6Zsxc/0ppHBOJSJyYQySXEF1iwVvmXNCmWhcPgB/DGuNLrVLIjHZhA//OIwBs3cgIjpe66IREWmCQZIrqNgecPcBIs8C4Qe1Lg3pmL+vB758vCE+7FkbXu5GrDt2BV0mb8DG4xFaF42IqMAxSHIFnr5ApXtTb3OUG2VjTqXHm5XD0iGtUDW4MK7cjMeTs7bh45VHkJiconXxiIgKDIMkV+xyI8qGaiWLYMlLrfBYs7Kql3b6PyfRd8YWnLsWq3XRiIgKBIMkV1H1fsBgBC7tB26c1bo05CB8PN0wvmcdTH+8Ify83bH33A10nbwBv++7oHXRiIjyHYMkV1EoCAhtnnqbC95SDnWpUwp/DG+NRuWK4WZ8EobO24ORv+1HbALnVCIi58UgyZVw9m3KgzLFfNU0AUPvrawmc/95xzl0n7oRhy9G4WLkLWw+GaGuiYichbvWBaACzkv6623g9Ebg1nXAp5jWJSIH4+5mxKudqqFFpUA1O/fJKzFqSROZT0kmlzAagAm96qBfk7KalfFiZByORxrUddkgD83KQUSOj0GSKwmoCJSoCVw+BBxfBdR9WOsSkYO6p1KQWtJk6Nzd2HTyatp2mXty5G8HsOlEBAp5eaigyWgwqGsZNWewuC/Xss1yH9kh42PS72/eZnufnaev47fd/8EEN3x5eL3mARsROTYGSa6mWtfUIOnIMgZJlCcBhTzxUvvK6YIkIS1KS/ddhNYkYHtr4QG0qVocpfx9tC4OETkgBkmumJe04VPgxBogMQ7w8Na6ROTAKhQvpFpwLFcvkQah59tWRCFPd7U9xWSCSS4qcDFZbIPqprPcx3w79flMSEm5cz/17xkeb7HtanQ8dp9Nv+ZcsgnYe/YGStVhkEREOccgydWENACKhAA3LwBh64GqnbQuETkwaaGRLq23Fh5EsskEN4MB43vV1qSLS5LGW370d7qATYxaeADenm5oX61EgZeJiBwbR7e5GknqME8seZSj3CjvJCDaOLI95g1qrq61ygEyB2wqt+l2EnlJPy/cuJWIAd/twAfLDiEhiTOGE1H2MUhy1bwk83xJ0p9BZIcARUa8aZ37IwHaP6+2wZCayer6n9fbo3+Lcupv32wMQ+/pmxEWEaNpGYnIcTBIckXlWwNefkB0OHB+l9alIbKrUv7eqOJvUtfeHm4Y16M2vn6yEYr6euDA+Ug8MGUDFu35T+tiEpEDYJDkitw9gSodU2/LKDciJ9epVkn8Maw1mlYIQExCMl6Zvw8jftmL6HjOGE5EmWOQBFfvcvtD65IQFYiQoj4qb+rlDlVUvtLC3efVjOEHz0dqXTQi0ikGSa5KWpKMHkDEMSDiuNalISoQbkYDXu5QVQVL0h0n+Uk9v9yEbzeGqSkGiIgsMUhyVd7+QIXWqbe5lhu5mGYVA1X3W8eawUhMNuH9ZYcwcPYONdcSEZEZgyRXZl7wll1u5IKKFfJUCd3v96gFT3cj1h69gi6TN2DziQiti0ZEOsEgyZWZ85LObQeiL2tdGqICJ+u+PdmiPJa81BKVSxTG5ZvxePzbbfjkzyNITOb0GESujkGSK/MLAUIapq62JXMmEbmoGqX8sHRISzzSJFQtdzJt7Un0+2oLzl2L1bpoRKQhBkmuzjz7NvOSyMX5errjo951MfXRBiji5a7Wges6ZQP+OKD9Yr1EpA0GSa6u+gOp16f+AeKjtS4Nkea61wvBH8Nbo35oUdyMS8KLc3ar9d9uJSRrXTQiKmAMklxd8epAsQpAcjxwco3WpSHShdAAXyx4oQUGt6ukljuct/0sHvxiI45euql10YioADFIcnVqwdvbo9yOcJQbkZmHmxFv3l8dPw5shuJFvHD8crQKlH7aeoZzKhG5CAZJdCdIOrYSSE7UujREutKqShBWDG+NdtWKIz4pBe8sPojBP+1GZCz/rxA5OwZJBIQ2A3wDgbgbwNktWpeGSHeCCnthVv8meKdbDXi4GbDy30voMnk9dpy+pnXRiCgfuXSQVL58edStWxf169dH+/bt4bKMbkDVLqm32eVGZJPRaMCzrSvit8H3oHygLy5ExqlpAqasOY7kFHa/ETkjlw6SxObNm7F3716sXbsWLs1yKgDmWxBlqm6Zolg2rDV6NigNiY0mrjqGx7/ZikuRcVoXjYjszOWDJLqtYnvA3QeIPAuEH9S6NES6VtjLHZ/3q4/P+taDr6cbtp66prrfVh8K17poROQKQdL69evRvXt3hISEqKUDFi9ebLXPtGnTVJeZt7c3mjVrhu3bt+foGPK8bdu2RZMmTTBnzhy4NE9foNK9qbc5sSRRtvRuVAbLhrZCrRA/XI9NxLM/7MTYpf8iPolzKhE5A90GSTExMahXr54KhGyZP38+RowYgTFjxmD37t1q386dO+Py5TtrkEmuUe3ata0uFy5cUH/fuHEjdu3ahaVLl2L8+PHYv38/XFraVAAMkoiyq2Lxwlj44j0Y2LKCuj9782n0nLYZJ69E42LkLWw+GaGutXQxMg7HIw3qmoiyzx061aVLF3XJzMSJEzFo0CAMGDBA3Z8xYwaWL1+OWbNmYeTIkWqb5BplpXTp0uq6VKlS6Nq1qwq2JJHblvj4eHUxi4qKUteJiYnqYk/m57P3895VxfvgbjDCcGk/EiNOAf6h0AvN6kTnWC/6qBP5tTnq/ipoXqEo3lx4EIcuRqHLpPVITDbJyogwGoAxD9RA30alYTQY1H1pyS4IC3b9h3eWHEKKyQ1fHl6PD3rURN9GZQrk2HrH/z+uWSeJOXhtBpMDzIomXyaLFi3CQw89pO4nJCTA19cXv/76a9o20b9/f9y4cQNLlizJVktVSkoKihQpgujoaNXtJoGWdL3ZMnbsWIwbN85q+9y5c1VZnEXLYx8iKOYo9pd5AmHFO2ldHCKHE5kAzDpqxOnouzfUG2BS87lKuKQu5tuG1MAr4zZb+6Xb/3bcZd5mSgEuqcYjQ7pjjm2YjKJe+VgJRDoWGxuLxx57DJGRkfDz83PMlqSsREREIDk5GcHBwem2y/0jR45k6znCw8PRs2dPdVueS1qlMguQxKhRo1T3nmVLUmhoKDp16nTXSs5NlLtq1Sp07NgRHh4eKEjGwNPA6tGo7X4GNbreHvGmA1rWiZ6xXvRZJ2VPXsXTs3fddT+ThCyWP1ML4CerHLNivWZoXjEQrk4PnxW9cYU6ibrdE5QdDhkk2UPFihWxb9++bO/v5eWlLhnJhyi/Pkj5+dyZqtldBUnGM5thTIoGfIpBTzSpEwfAetFXnVQr5a+61CynT5L7K19ugxJFvNT2FJNJXSQwsrxvSrudem1K25bzfSKi4/Hy/L1Ws3p8teE0apUJQEAhzwKvGz3i/x/XqhOPHLwuhwySgoKC4ObmplqDLMn9kiVLalYupxBQEShRE7h8CDj2F1Cvn9YlInI4pfx9MKFXHby18CCSTSa4GQwY36s2qgYXKfCyxCUmY9TCAyqASu2WM2DjiatqyoJJ/RqgRSW2KBE53Oi2rHh6eqJRo0ZYs+bOqvWSXyT3W7RooWnZnEK1291sRznKjSi3+jUpi40j22PeoObqWu5rVY5/Xm2DITWTse7VNvh9aCtULF4I4VHxeOybrZj411EkJadoUjYivdNtkCTJ1DI6zTxCLSwsTN0+e/asui/5QTNnzsT333+Pw4cPY/DgwSoZ2zzajewwFcCJNUAihwwT5aVFSVpq5Frbcnijir9JXdcM8VNzOz3cuIzqhpvy9wk88vVWnL+h7TQFRHqk2yBp586daNCggbqYgyK5PXr0aHW/X79++PTTT9V9mQ9JAqiVK1daJXNTLoQ0AIqEAAnRQNh6rUtDRHbm6+mO//WphymPNlCzh+88c11NWbDy4EWti0akK7oNktq1a3c7GTH9Zfbs2Wn7DBkyBGfOnFHzF23btk3Nuk12IIkL5rXc2OVG5LQerBeCP4a1Rr3QooiKS8ILP+3GO4sPqDwmItJxkEQ6yUv6dwlw45zWpSGifFI20Be/vtACz7etqO7/tPUsenyxCcfCb2pdNCLNMUgi266fSb2Ouw5Mrgvs/kHrEhFRPvFwM2JUlxr4YWBTBBX2wtHwm3jwi42Yu+2sasEnclUMksha5Hngj1fv3Jdpe39/OXU7ETmtNlWLY8Xw1mhdJQhxiSl4a9EBDJm7B5G3nHeJCqKsMEgia9dOpgZGlkzJwLVTWpWIiApI8SJe+H5AU4zqUh3uRgOWH7iIrpM3YNeZ61oXjajAMUgiawGVAEOGj4bBLXWiSSJyekajAc+3rYTfBt+DsgG+anqAh7/agmlrTyDZchpxIifHIIms+ZcGuk9OHyh1m5i6nYhchox6Wz6sFXrUD1HB0Sd/HsWT325DeBTnTyPXwCCJbGv4FDB8P2C8vbZThdZal4iINFDE2wOT+tXHJ33qwsfDDZtPypImG/D3kfTLQhE5IwZJlLmioUDxaqm3I45rXRoi0ojBYEDfxqFYNqwVapbyw7WYBAycvRPvLzuE+CTOqUTOi0ESZS2ocur1VQZJRK6uUvHCWPjiPXj6nvLq/rcbw9B7+macuhKtddGI8gWDJMpaUNXU64hjWpeEiHTA28MNYx+shW+eaoxivh44eD4KD0zdiN92/ad10YjsjkESZTNIYksSEd3RoWYwVgxvg2YVAhCbkIxXF+zDK/P3Ijo+SeuiEdkNgyTKWuDt7jYGSUSUQUl/b8wd1BwjOlaF0QAs2nMeD0zZgAP/RWpdNCK7YJBE2QuSYiOA2Gtal4aIdMbNaMCw+6pg/vMtEOLvjdNXY9Fr+iZ8s+EUUjinEjk4BkmUNa/CgN/t+ZGuntC6NESkU03KB+CP4a3RuVYwEpNN+GD5YQz8fgciouO1LhpRrjFIorsLqpJ6zeRtIspCUV9PzHiiET54qDa83I345+gVNafSxuMRWheNKFcYJNHdcYQbEeVgTqUnmpfD0iGtUKVEYVy5GY8nZ23DxyuPIDE5w5qQRDrHIInuLtDcksTuNiLKnmoli6hA6dGmZWEyAdP/OanWf9t15ho2n4zAxchbWhcRFyPjcDzSoK6JbHG3uZXIErvbiCgXfDzdMKFXHbSqHISRC/djz9kb6D19i/qbAUDXOqXQoGxR1foko+OMt69T79/ZZjD/zWi+b1CPT7//nX0ye7x6jDF1+5rDlzF93UmYTG748vB6Vc5+TcpqXWWkMwySKPtB0vUwIDkRcPPQukRE5EC61S2Fkv5eaQGSkHFvyw9cVBetySC8txYeRJuqxVHK30fr4pCOMEiiuysSAngUAhJjgOun7wRNRETZFJ9kOx+pZaVABBb2QorJpLrl5Dr1AnXfZHHf9j6W28z7Z7x/Zx+5jklIQnhU+lF3ySYTTkfEMEiidBgk0d1J+7Ws4XZxX2qXG4MkIsqhCkGFVDeX5dRJbgYDPn24XoEHJpIP1fKjv9OVRXyzIQy1SvvDz5ut5ZSKiduUw+RtzrxNRDkngZDk/UhgJOR6fK/amrTcmMsiQZtIzW8C1hy5jG5TNmDP2esFXibSJ7YkUfZwDTciyiNJjJa8n9MRsSgf5Ktp15aUpUWFYvjlj7V4uGt7XI1NwtB5e3Du2i30nbEFr3aqhufbVFSJ3uS62JJE2SPdbeIqgyQiyj0JjFpUCtRF7k8pf29U8Tep6wZli6kZwx+oWwpJKSY1r9NTs7bj8k1OD+DKGCRRzlqSrhxNzaYkInIykos09dEG+F/vuvDxcMPGExHoMmkD/jl6WeuikUYYJFH2BFRKvY67AcRe1bo0RET5QuZYerhJKH4f2hLVSxbB1ZgEPP3dDny4/BASMhmhR86LQRJlj6cv4H97ojXmJRGRk6tcoggWv9QS/VuUU/dnbghDnxmb1TQB5DoYJFH2ceZtInIh3h5uGNejNr5+shGK+npg/3+RavTb4j3ntS4aFRAGSZTzIInJ20TkQjrVKok/hrVG0woBiElIxsvz9+LVX/YhJj5J66JRPmOQRLloSWKQRESuJaSoD+YNao6XO1RRcyr9tvs/dJ+6EQfPR2pdNMpHDJIo+zihJBG5MDejAS93qKqCJZk24FREDHp9uRnfbgxTy5+Q82GQRDmfBkDWb0tKv+4REZGraFYxUHW/dawZjITkFLy/7BCe+X4nrkbze9HZMEii7CtSEvAsApiSgWthWpeGiEgzxQp5qoTu93rUgqe7EX8fuYwukzdg88kIrYtGdsQgibJP1lzizNtERGlzKj3VojwWv9gSlYoXwuWb8Xj8m2349M+jSErmnErOgEES5XINN04DQEQkaob44fehrfBIk1C1IMEXa0+g39db8d/1WK2LRnnEIIlymbx9QuuSEBHphq+nOz7qXVcta1LEyx27zlxH18kbsOLARa2LRnnAIIlyhhNKEhFlqnu9ELVQbv3QooiKS8LgObsxauEB3EpI1rpolN9BktFohJubW7Yv5v3fe+896M3Ro0dRv379tIuPjw8WL16sdbEcqLvtOBe6JSKyITTAFwteaIHB7SqpVM5528+ix7SNOHrpptZFoxxyz8nOYWG5G9FUtGhR6E21atWwd+9edTs6Ohrly5dHx44dtS6W/gVUlHRFID4SiLkCFC6hdYmIiHTHw82IN++vjnsqBWLEL/twLDwaD36xEe8+UBOPNyurkr7JyYKkp59+OldvrDzuqaeegl4tXboU9913HwoVKqR1UfTPwxsoVi51riTpcmOQRESUqdZVimPF8NZqGZN1x67gncUHselEBD7qVRf+vh5aF4/sHSTlRr169XL8mPXr1+OTTz7Brl27cPHiRSxatAgPPfRQun2mTZum9rl06ZI6xtSpU9G0adMcH+uXX37RdRCny+RtFSQdB8q30ro0RES6FlTYC9893UTNzP2/P49gxcFLarHcyY/UR+PyAVoXj+wVJPXv3x8FJSYmRgU+AwcORK9evaz+Pn/+fIwYMQIzZsxAs2bNMGnSJHTu3FnlGpUokdq6IblGSUnWCxD+9ddfCAkJUbejoqKwefNm/PzzzwXwqpwoL+nEKi5PQkSUTUajAYPaVESzigEYOm8PzlyNVdMEvHxfFfRsWBpnr8WiQlAhlPL30bScFyPjcDzSoK7LBrGlK0dBUkHq0qWLumRm4sSJGDRoEAYMGKDuS7C0fPlyzJo1CyNHjlTbzDlHWVmyZAk6deoEb2/vLPeLj49XFzMJrkRiYqK62JP5+ez9vPZiKFZRfXBSrhxFcgGVUe91ohXWizXWiTXWiX7qpUZwISx6oTnG/n4YS/dfxGerjqmLkIVzP+hRE30blYEWFuz6D+8sOYQUkxu+PLxe07Lkp5y83wZTLlblS0lJwbp167BhwwacOXMGsbGxKF68OBo0aIAOHTogNDQ0p0+ZdSENhnTdbQkJCfD19cWvv/6argtOWrpu3LihAp/s6t69O5577jl1nZWxY8di3LhxVtvnzp2ryuJKAm8eQasT4xHjWQKra32qdXGIiByOnHnXXTRg0RkZZG6Z62tCUU/A3Xhn+LmkAhtuXxst72f4251tJqv91fPcDsRsPS4xGTh4w/wM5v1NGNswGUW94FQkZnnssccQGRkJPz8/+7Uk3bp1C5999hmmT5+Oa9euqe4s6baS4fMnTpxQQ+ildUdaZkaPHo3mzZsjP0RERCA5ORnBwcHptsv9I0eOZPt5pIK2b9+O33777a77jho1SnXvWbYkSTAor/VulZybKHfVqlVqtJ2Hhw6bO6MbA5PHwzfhCrp2uhdwz7oVziXqRCOsF2usE2usE33WS+Cpa1j03c4MWw24kZDXZ7bPyDkTDKhUvzmaVXCuvClzT1B25ChIqlq1Klq0aIGZM2dm+qGSliVpXXnkkUfw9ttvq6BJr/z9/REeHp6tfb28vNQlI6mD/PrPlZ/PnSdFQwAvfxjiI+ERdQ4Irllgh9ZtnWiM9WKNdWKNdaKveqlc0k+17KRY9OfI/RlPNEJgYU+1PSXFpK6l00fdV9cm1RJlggkpKeZtd99H7pv3Tb1/53ZkbCImrzmOjF1LJ6/eQquqzvWZycl7naMgSRKea9SokeU+5cqVU60ur732Gs6ePYv8EBQUpCapzBjgyP2SJUvmyzEp40K3VYDzO1OnASjAIImIyFlIkvaEXnXw1sKDSDaZ4GYwYHyv2uhUS5vzWKmi3mp2cMugbcySf3Hwv0iM61FLLb3ianI047ZlgJRV4pN0h0mkVqlSJeQHT09PNGrUCGvWrEmXJyX3paWLCnjmbSIiypV+Tcpi48j2mDeoubqW+1qW5Z9X22BIzWSsfaUVht1XRf0mloTuB6ZuxL8XIuFqcr12m3Sn2cr5ltacdu3a5bVcahZsGZ1mHqEms33LbXPrlOQHSbff999/j8OHD2Pw4MFq2gDzaDfKZ0GVU6+vMkgiIspri1KLSoGaD/9PLYs3qvibUCbAFyM6VsXcZ5ujpJ83Tl2JQc9pmzF7U5jNc7+zynWQJMHKs88+m26bTOooAVL16tXzXLCdO3eq0XJyMQdFclsSwkW/fv3w6aefqvuSQC4B1MqVK62SuSm/W5K40C0RkbNqUSlQLdjboUYJJCSnYOzvhzDoh124HpPn7HLnDpL++OMPNQmjecTXhQsX0LZtW9SpU0fNYJ1XEmxJtJrxMnv27LR9hgwZohLFZf6ibdu2qUklqQBn3RYRJ7jQLRGREwso5ImZTzXG2O414elmxOrD4egyeQO2nroKZ5frLCyZF0kSuVu1Sl2WYtmyZWjYsCHmzJkDozHXsRc5ioAKgMENSLgJ3LwE+JXSukRERJRPDAYDnm5ZAU0qpM4YLt1vj83ciiH3VsGweyvD3c05z/t5elUyT5DMMSGBkayZNm/ePDXqjFyAuxdQrHzqbXa5ERG5hFoh/lg2tJWaiVtGwU1ZcxyPztyK8zduAa4eJBUrVgwBAQHpLjJhpEzK+PvvvyMwMDBtO7kAmQZAMHmbiMhl+Hq645O+9dQCvYW93LHj9HV0nbwBKw9egkt3t8kiskTpgqRjKzkNABGRC+pRvzTqhxbFsHl7sO+/SLzw0y480bws3ulWE94ebq4XJMnaaDn10Ucf4YUXXkDRokVz/FhylORtBklERK6oXGAhLHjhHny26ii+WncKP209i52nr2Pqow1QJbgIHF2+Z1qNHz9erfNGTogTShIRuTxPdyNGdamBHwY2RVBhTxy5dBPdv9iIedvPOvycSvkeJDl6BVE2gqTIs0BCrNalISIiDbWpWhwrhrdB6ypBiEtMUUucDJm7B5G3Ml+hQ++cc8weFYxCgYBPsdTb105qXRoiItJY8SJe+H5AU4zqUh3uRgOWH7iokrp3nbkOR8QgifKGM28TEZEFo9GA59tWwq+D70HZAF81PcDDX23BtLUnkGy5eq4DYJBE9pt5m4iI6DYZ+bZ8WCs8WC9EBUef/HkUT83ahvCoODgKBklkn7mS2JJEREQZFPH2UPMp/a9PXfh4uGHTiatqSZO1Ry7DEeR7kNS6dWv4+Gi/sjHlE3a3ERHRXZY0ebhxKH4f2go1SvnhWkwCBszegfeXHUJ8UjKcMkiyXGjWUlJSEkaNGpVuIdxSpbiul/PPun0CSEnRujRERKRTlUsUxqIX78HT96QuafXtxjD0nr4ZYRExcLogadiwYejbty+uX7+TsX706FE0a9ZMreFGLkLWbzO6A4mxwM0LWpeGiIh0zNvDDWMfrIWZTzVGUV8PHDwfhQembMDC3f/BqYKkPXv24L///kOdOnXUIrfTpk1Dw4YNUb16dezbt8++pST9cvMAilVIvc1JJYmIKBs61gzGiuGt0axCAGISkjHil30YMX8vouOT4BRBUqVKlbBp0yb06tUL999/P1555RV88803mDNnDvz9/e1bStI3zrxNREQ5VMrfB3MHNceIjlVhNAAL95xXrUoH/ouEUyRuL1++HD///DNatGih1mb79ttvceECu1xcDke4ERFRLrgZDRh2XxXMf74FQvy9cfpqLHpN34RvNpzC+eux2HwyAhcjb8HhgqTnn39e5SS9+eab2LBhA/bv3w9PT0/V/fbLL7/Yt5TkIMnbbEkiIqKca1I+AH8Mb43OtYKRmGzCB8sPo+XHa/HYzG1o+dHfmL/jLBwqSJKutm3btuHVV19Vw/tKliypRrK99957GDhwoH1LSfrG7jYiIsqjor6emPFEI7zWuVq67TJJ91sLD2rSouSe2wfu2rULXl5eVttfeukldOjQIa/lIkcSWDn1Ouo8EB8NeBXWukREROSADAYDGpYtarU92WTC6YhYlcfkEC1JtgIks2rV0keB5OR8AwDfoDvzJREREeVShaBCKpHbkpvBgPJBvihoOQqSZBTb1q1b77rfzZs38fHHH6tpAchFsMuNiIjsQFqLJvSqowIjIdfje9Uu8FakHHe3SaJ279691RD/7t27o3HjxggJCYG3t7eaVPLQoUPYuHGjyk3q1q0bPvnkk/wrOelLUGXg7GYmbxMRUZ71a1IWbaoWV11s0oKkRYCU4yDpmWeewRNPPIEFCxZg/vz5+PrrrxEZGZnWj1izZk107twZO3bsQI0aNfKrzKRHXMONiIjsSAIjrYKjXCduSy6SBEpyERIk3bp1C4GBgfDw8MiPMpIjCDTPlcScJCIicg65StxOTExUw/zDwsJU15sM/2eA5OIs50riQrdEROSqQZIERL/99pv9S0OOq2g5wM0TSIoDIs9pXRoiIiLtpgB46KGHsHjx4ryXgJyDmzsQUDH1NpO3iYjICeR6MskqVaqo2bVl5u1GjRqhUKFC6f4+bNgwe5SPHK3L7cqR1GkAKnNCUSIictEgSRazlUVtZeZtuViSkW4Mklw5eZstSURE5MJBkiRtE6XDaQCIiMhVg6SzZ3O3Cq+0OPn5+eXqseRAOOs2ERG5apBUvnz5HB9Aut7GjBmD0aNH5/ix5ICzbovoS0BcFODNwJiIiFwkSErh/DeUFW9/oHAwEB2eOsKtdCOtS0RERFQwQVKFChVUy1BOvfzyy0zkdqXkbQmSZOZtBklEROQqQdLs2bNzdZDcdNORA08DcGYjk7eJiMi1gqS2bdvCmXz66af47rvvVOvYyJEj09ajozzgCDciInL1KQAc3YEDBzB37lw1x5PJZEL79u3xwAMPqJF4ZI813LjQLRERueiyJI7u8OHDaNGiBby9veHj44N69eph5cqVWhfLiYKkk0BKstalISIicr4gaf369ejevTtCQkJUd5itdeKmTZum8p0k0GnWrBm2b9+e7eevXbs2/vnnH9y4cQPXr19Xt8+fP2/nV+GC/EMBNy8gOR64kbt5tYiIiPRAt91tMTExqnVn4MCB6NWrl9Xf58+fjxEjRmDGjBkqQJo0aRI6d+6Mo0ePokSJEmqf+vXrIykpyeqxf/31F2rWrKlG3N17773w9/dH8+bN4ebmViCvzakZ3YDAysDlf1MnlQyooHWJiIiInCtI6tKli7pkZuLEiRg0aBAGDBig7kuwtHz5csyaNUslYYu9e/dmeYznn39eXcSzzz6rFu3NTHx8vLqYRUVFqevExER1sSfz89n7eQuKW2BlGC//i+TLh5FSob1dntPR6yS/sF6ssU6ssU5sY724Zp0k5uC1GUyStaxz0t22aNEiPPTQQ+p+QkICfH198euvv6ZtE/3791fdZ0uWLMnW816+fFm1OknrU9++fbF79264u9uOG8eOHYtx48ZZbZfkbykL3VH9wq+oFr4UpwPbY1/Z1CCWiIhID2JjY/HYY48hMjLyrkum6bYlKSsRERFITk5GcHBwuu1y/8iRI9l+nh49eqhKKlSokJoKILMASYwaNUp171m2JIWGhqJTp052X5dOotxVq1ahY8eO8PDwgKMxHIwBlixF2UJxKN21q12e09HrJL+wXqyxTqyxTmxjvbhmnUTd7gnKDocMkuxly5Yt2d7Xy8tLXTKSD1F+fZDy87nzVYnq6sp49SSMdi6/w9ZJPmO9WGOdWGOd2MZ6ca068cjB69Lt6LasBAUFqSTr8PDwdNvlfsmSJTUrF2WYBiDmMnDrhtalISIiyhWHDJI8PT3RqFEjrFmzJt3iu3Jf5j4ijXkVAYqEpN7mpJJEROSgdNvdFh0djRMn7pxgw8LC1Gi1gIAAlC1bVuUHSaJ248aN0bRpUzUFgEwbYB7tRhoLqgzcvJC6PEmZxlqXhoiIyHmCpJ07d6qlQszMSdMSGMlCu/369cOVK1cwevRoXLp0Sc2JJDNmZ0zmJg3XcAtbzzXciIjIYek2SGrXrp1aUy0rQ4YMURfSocDbeUkyoSQREZEDcsicJHKg5G0GSURE5KAYJFH+BknXTgHJ1kvDEBER6R2DJMoffmUAdx8gJRG4cUbr0hAREeUYgyTKH0Zj6gg3weRtIiJyQAySKP8weZuIiBwYgyTK32kABFuSiIjIATFIovxP3uas20RE5IAYJFEBTAPAliQiInI8DJIo/wTeTtyOvQrEXtO6NERERDnCIInyj2eh1KkABJO3iYjIwTBIovzFLjciInJQDJKogJK32ZJERESOhUESFdA0AAySiIjIsTBIovzF7jYiInJQDJKoYGbdvn4aSE7UujRERETZxiCJ8pdfCOBRCEhJAq6FaV0aIiKibGOQRPnLYLiz0C2Tt4mIyIEwSKL8xzXciIjIATFIovzHEW5EROSAGCRRwS1PwiCJiIgcCIMkKtjuNpNJ69IQERFlC4Mkyn+BlSSDG4i7kbrYLRERkQNgkET5z8MHKBqaepvJ20RE5CAYJFHB4Ag3IiJyMAySqGBn3mbyNhEROQgGSVTAa7gxSCIiIsfAIIkKNkjirNtEROQgGCRRweYkyUK3SfFal4aIiOiuGCRRwSgcDHj5AaYU4NoprUtDRER0VwySqOAWuuXM20RE5EAYJFHB4TQARETkQBgkUcEJut2SdPWE1iUhIiK6KwZJVHDYkkRERA6EQRJpECQd50K3RESkewySqOAEVAQMRiA+Coi+rHVpiIiIssQgiQqOuxdQtFzqbXa5ERGRzjFIooLFmbeJiMhBuESQ1LNnTxQrVgx9+vTJ0d8on/OSiIiIdMwlgqThw4fjhx9+yPHfKD8XumV3GxER6ZtLBEnt2rVDkSJFcvw3ygeB5iCJLUlERKRvmgdJ69evR/fu3RESEgKDwYDFixdb7TNt2jSUL18e3t7eaNasGbZv365JWcmO3W03zgKJt7QuDRERkX6DpJiYGNSrV08FQrbMnz8fI0aMwJgxY7B79261b+fOnXH58p0h5PXr10ft2rWtLhcuXCjAV0LZUigI8PYHYOJCt0REpGvuWhegS5cu6pKZiRMnYtCgQRgwYIC6P2PGDCxfvhyzZs3CyJEj1ba9e/fmeznj4+PVxSwqKkpdJyYmqos9mZ/P3s+rF26BVWA8vxNJ4YdhCrjdsuTidZJbrBdrrBNrrBPbWC+uWSeJOXhtmgdJWUlISMCuXbswatSotG1GoxEdOnTAli1bCrQsEyZMwLhx46y2//XXX/D19c2XY65atQrOqMEtH5QFcHzLchwL88jRY521TvKK9WKNdWKNdWIb68W16iQ2NtY5gqSIiAgkJycjODg43Xa5f+TIkWw/jwRV+/btU117ZcqUwYIFC9CiRYu7/s2SBGrS7WfZkhQaGopOnTrBz88P9o5y5QPasWNHeHjkLIhwBMbNx4G1G1At0IjKXbtm6zHOXie5xXqxxjqxxjqxjfXimnUSdbsnyOGDJHtZvXp1rv5mycvLS10ykg9Rfn2Q8vO5NVWiuroyXj0BYw5fn9PWSR6xXqyxTqyxTmxjvbhWnXjk4HVpnridlaCgILi5uSE8PDzddrlfsmRJzcpF9pp1+wQXuiUiIt3SdZDk6emJRo0aYc2aNWnbUlJS1H1bXWLkIIpVAAxuQEI0cPOi1qUhIiLSZ3dbdHQ0Tpw4kXY/LCxMjVYLCAhA2bJlVR5Q//790bhxYzRt2hSTJk1S+UPm0W7kgNw9gYAKqS1JMvO2X4jWJSIiItJfkLRz5060b98+7b45OVoCo9mzZ6Nfv364cuUKRo8ejUuXLqk5kVauXGmVzE0OOPO2CpKOAxXbaV0aIiIi/QVJsiyI6S55KUOGDFEXcrK8pGMruDwJERHplq5zksgVkrcZJBERkT4xSCJt13BjSxIREekUgyTSNkiKPAckxGhdGiIiIisMkkgbvgGAT0Dq7asntS4NERGRFQZJpIMut2Nal4SIiMgKgyTSTlDl1GuZCoCIiEhnGCSRdtiSREREOsYgibTDIImIiHSMQRJpO+u2OXE7JUXr0hAREaXDIIm0U6wcYPQAEmOBqPNal4aIiCgdBkmkHTeP1IVuBWfeJiIinWGQRNrizNtERKRTDJJIH2u4MUgiIiKdYZBE+kje5gg3IiLSGQZJpC12txERkU4xSCJ9zLp98wIQf1Pr0hAREaVhkETa8ikGFCqeepvLkxARkY4wSCIddbkxSCIiIv1gkETaC7zd5cbkbSIi0hEGSaQ9ruFGREQ6xCCJ9DNXEnOSiIhIRxgkkb6CJC50S0REOsEgibRXtBzg5gkkxQGR57QuDRERkcIgibRndAMCKqXe5qSSRESkEwySSGdruDF5m4iI9IFBEuksL4ktSUREpA8MkkgfuIYbERHpDIMk0odAc3cbgyQiItIHBkmkr4Vuoy8BcZFal4aIiIhBEumEtz9QuGTqba7hRkREOsAgifSDydtERKQjDJJIPzgNABER6QiDJNIPJm8TEZGOMEgi/eA0AEREpCMMkkh/3W3XTgIpyVqXhoiIXByDJNIP/1DA3RtITgBunNG6NERE5OIYJJF+GI1A4O35ktjlRkREGnOJIKlnz54oVqwY+vTpk277jRs30LhxY9SvXx+1a9fGzJkzNSsj3cYgiYiIdMIlgqThw4fjhx9+sNpepEgRrF+/Hnv37sW2bdswfvx4XL16VZMyUsbkbU4DQERE2nKJIKldu3YqIMrIzc0Nvr6+6nZ8fDxMJpO6kIY4wo2IiHRC8yBJWnK6d++OkJAQGAwGLF682GqfadOmoXz58vD29kazZs2wfft2ux1futzq1auHMmXK4PXXX0dQUJDdnpvysIYbZ90mIiJXD5JiYmJUkCKBkC3z58/HiBEjMGbMGOzevVvt27lzZ1y+fDltH3NOUcbLhQsX7nr8okWLYt++fQgLC8PcuXMRHh5u19dHuZxQMuYKcOu61qUhIiIX5q51Abp06aIumZk4cSIGDRqEAQMGqPszZszA8uXLMWvWLIwcOVJtk5yivAoODlYB2IYNG6wSvM3dcXIxi4qKUteJiYnqYk/m57P38zoEoxfci5SC4eZFJIUfgal0Y7XZpeskC6wXa6wTa6wT21gvrlkniTl4bZoHSVlJSEjArl27MGrUqLRtRqMRHTp0wJYtW/L8/NJqJDlJkq8UGRmpuv4GDx5sc98JEyZg3LhxVtv/+uuvtLwme1u1ahVc0T2mYiiOi9j/9284F3inxdCV6+RuWC/WWCfWWCe2sV5cq05iY2OdI0iKiIhAcnKyauWxJPePHDmS7eeRoEq61KRrT3KPFixYgBYtWuDMmTN47rnn0hK2hw4dijp16th8DgnUpNvPsiUpNDQUnTp1gp+fH+wd5coHtGPHjvDw8ICrMa5cB+w6hHqlfVDn3q5qm6vXSWZYL9ZYJ9ZYJ7axXlyzTqJu9wQ5fJBkL6tXr7a5vWnTptnuqvPy8lKXjORDlF8fpPx8bl0rUU1duV0/BbcMr99l6+QuWC/WWCfWWCe2sV5cq048cvC6NE/czoqMNJNh+hmTqeV+yZIlNSsXFdAabpwriYiINKTrIMnT0xONGjXCmjVr0ralpKSo+9JdRk4+wu1aGJDsvMmDRESkb5p3t0VHR+PEiRNp92UovnSBBQQEoGzZsioPqH///mr5EOkemzRpksotMo92IyfkVxrw8AUSY4HrZ+7MnURERORKQdLOnTvRvn37tPvm5GgJjGbPno1+/frhypUrGD16NC5duqTmRFq5cqVVMjc54UK3l/andrkxSCIiIlcMkmTJkLstBTJkyBB1IRfLS5IgiTNvExGRRnSdk0QujAvdEhGRxhgkkT5Jd5uIuJOvRkREVJAYJJE+sSWJiIg0xiCJ9N2SdOsaEHNV69IQEZELYpBE+uTpC/iHpt5m8jYREWmAQRLpF2feJiIiDTFIIv3PvB3BliQiIip4DJLIAVqSGCQREVHBY5BE+sURbkREpCEGSaT/lqTrp4HkBK1LQ0RELoZBEulXkVKAZ2HAlJwaKBERERUgBkmkXwZD2nxJhquceZuIiAoWgyRyiLwkA+dKIiKiAsYgifSNQRIREWmEQRLpW9Dt5UnY3UZERAWMQRI5TkuSyaR1aYiIyIUwSCJ9C6goIRIMcZHwTLqpdWmIiMiFMEgiffPwAYqWVTeLxF/QujRERORCGCSRw3S5FY67qHVJiIjIhTBIIoeZeZtBEhERFSQGSeQ4QVI8gyQiIio4DJJI/wJTgyT/2DNAFPOSiIioYDBIIv27uE9d+STdgPsX9YHdP2hdIiIicgEMkkjfIs8Dq95Nu2swpQC/v5y6nYiIKB8xSCJ9u3YSkMDIkikZuHZKqxIREZGLYJBE+hZQCTBk+Jga3G5PMklERJR/GCSRvvmXBrpPhkkCI2lEkuvuk1K3ExER5SP3/HxyIrto+BSSyrXFthXz0KzLo/AILKd1iYiIyAWwJYkcg18Irhapoa6JiIgKAoMkIiIiIhsYJBERERHZwCCJiIiIyAYGSUREREQ2MEgiIiIisoFBEhEREZENDJKIiIiIbGCQRERERGQDgyQiIiIiGxgkEREREdnAIImIiIjIBi5wm0smk0ldR0VF2f25ExMTERsbq57bw8PD7s/viFgntrFerLFOrLFObGO9uGadRN0+b5vP41lhkJRLN2/eVNehoaFaF4WIiIhycR739/fPch+DKTuhFFlJSUnBhQsXUKRIERgMBrtHuRJ8nTt3Dn5+fnZ9bkfFOrGN9WKNdWKNdWIb68U168RkMqkAKSQkBEZj1llHbEnKJanYMmXK5Osx5APqrB/S3GKd2MZ6scY6scY6sY314np14n+XFiQzJm4TERER2cAgiYiIiMgGBkk65OXlhTFjxqhrSsU6sY31Yo11Yo11YhvrxRrrJD0mbhMRERHZwJYkIiIiIhsYJBERERHZwCCJiIiIyAYGSUREREQ2MEjSmWnTpqF8+fLw9vZGs2bNsH37driyCRMmoEmTJmpm8xIlSuChhx7C0aNHtS6Wrnz00Udq1veXX34Zruz8+fN44oknEBgYCB8fH9SpUwc7d+6EK0tOTsa7776LChUqqDqpVKkS3n///WytWeUs1q9fj+7du6vZleX/yeLFi9P9Xepi9OjRKFWqlKqjDh064Pjx43DlepH129588031f6hQoUJqn6eeekqtMuFqGCTpyPz58zFixAg1/HL37t2oV68eOnfujMuXL8NVrVu3Di+99BK2bt2KVatWqf+8nTp1QkxMjNZF04UdO3bgq6++Qt26deHKrl+/jpYtW6oFOVesWIFDhw7hs88+Q7FixeDKPv74Y0yfPh1ffPEFDh8+rO7/73//w9SpU+Eq5LtCvkvlB6gtUh9TpkzBjBkzsG3bNhUUyPduXFwcXLVeZIFbOQe9++676nrhwoXqx+mDDz4IlyNTAJA+NG3a1PTSSy+l3U9OTjaFhISYJkyYoGm59OTy5cvyE9i0bt06k6u7efOmqUqVKqZVq1aZ2rZtaxo+fLjJVb355pumVq1aaV0M3enWrZtp4MCB6bb16tXL9Pjjj5tckXx3LFq0KO1+SkqKqWTJkqZPPvkkbduNGzdMXl5epnnz5plctV5s2b59u9rvzJkzJlfCliSdSEhIwK5du1RTr+X6cHJ/y5YtmpZNTyIjI9V1QEAAXJ20sHXr1i3dZ8ZVLV26FI0bN0bfvn1Vt2yDBg0wc+ZMuLp77rkHa9aswbFjx9T9ffv2YePGjejSpYvWRdOFsLAwXLp0Kd3/IVnTS1Id+L2bnnz3Srdc0aJF4Uq4wK1OREREqPyB4ODgdNvl/pEjRzQrl56kpKSovBvpVqlduzZc2c8//6yawaW7jYBTp06pbiXprn7rrbdUvQwbNgyenp7o378/XNXIkSPVqu7Vq1eHm5ub+o758MMP8fjjj2tdNF2QAEnY+t41/42guh4lR+nRRx916kVvbWGQRA7VcnLw4EH1S9iVnTt3DsOHD1c5WpLgT6kBtLQkjR8/Xt2XliT5rEieiSsHSb/88gvmzJmDuXPnolatWti7d6/6oSGJuK5cL5R9iYmJePjhh1WCu/wQcTXsbtOJoKAg9UsvPDw83Xa5X7JkSbi6IUOGYNmyZVi7di3KlCkDVybdspLM37BhQ7i7u6uLJLhL8qncltYCVyMjk2rWrJluW40aNXD27Fm4stdff121Jj3yyCNqpNKTTz6JV155RY0aJaR9t/J7N+sA6cyZM+pHmau1IgkGSToh3QKNGjVS+QOWv47lfosWLeCq5NeLBEiLFi3C33//rYYyu7r77rsPBw4cUK0C5ou0okgXityWYNvVSBdsxqkhJA+nXLlycGUySklyGy3J50O+Wwjq+0SCIcvvXemelFFurvy9axkgHT9+HKtXr1ZTa7gidrfpiORTSBO4nPCaNm2KSZMmqWGaAwYMgCt3sUlXwZIlS9RcSeY8AUmulDlNXJHUQ8acLBm2LF9irpqrJa0jkqQs3W3yxS7zi3399dfq4spkHhzJQSpbtqzqbtuzZw8mTpyIgQMHwlVER0fjxIkT6ZK15ceEDP6QepHuxw8++ABVqlRRQZMMe5fuSJmTzVXrRVpm+/Tpo/IepQVfWqfN373yd/lR7zK0Hl5H6U2dOtVUtmxZk6enp5oSYOvWrSZXJh9RW5fvvvtO66LpiqtPASB+//13U+3atdXw7erVq5u+/vprk6uLiopSnwv5TvH29jZVrFjR9Pbbb5vi4+NNrmLt2rU2v0P69++fNg3Au+++awoODlafnfvuu8909OhRkyvXS1hYWKbfvWvXrjW5EoP8o3WgRkRERKQ3zEkiIiIisoFBEhEREZENDJKIiIiIbGCQRERERGQDgyQiIiIiGxgkEREREdnAIImIiIjIBgZJROQQ2rVrp2ZH1hODwYDFixdrXQwiyiecTJKIHMK1a9fg4eGhlmUpX768CpgKKmgaO3asCoZk2QZLslRDsWLF4OXlVSDlIKKCxbXbiMghyJpR9paQkJCndai4UjyRc2N3GxE5VHebXJ85c0YtaivdXXIx27hxI1q3bq0WPw4NDcWwYcPUItFm0gL1/vvv46mnnoKfnx+ee+45tf3NN99E1apV4evri4oVK6pFTmUVdDF79myMGzcO+/btSzuebLPV3XbgwAHce++96viy4LA8vywkavb000+rhVM//fRTtYio7COLOJuPRUT6wiCJiBzKwoULUaZMGbz33nu4ePGiuoiTJ0/i/vvvR+/evbF//37Mnz9fBU1DhgxJ93gJUOrVq4c9e/aoYEhIF54EPocOHcLkyZMxc+ZMfP755+pv/fr1w6uvvopatWqlHU+2ZSTBWOfOnVX3244dO7BgwQKsXr3a6vhr165VZZXr77//Xh3XHHQRkb6wu42IHK7bzc3NTQU2lt1dEyZMwOOPP56Wp1SlShVMmTIFbdu2xfTp0+Ht7a22S0uPBD2W3nnnnXStTa+99hp+/vlnvPHGG6pVqHDhwnB3d8+ye23u3LmIi4vDDz/8gEKFCqltX3zxBbp3746PP/4YwcHBapsEUbJdXkP16tXRrVs3rFmzBoMGDbJzTRFRXjFIIiKnIN1h0oI0Z86ctG0yLiUlJQVhYWGoUaOG2ta4cWOrx0qrkwRU0sIj3WNJSUmqOy4nDh8+rFqozAGSaNmypTr+0aNH04IkaZGSAMlMut2km46I9IdBEhE5BQlunn/+eZWHlFHZsmXTblsGMWLLli2qBUryjqS7zN/fX7UiffbZZ/lSThmhZ0nymiSQIiL9YZBERA5HRqQlJyen29awYUOVU1S5cuUcPdfmzZtRrlw5vP3222nbJDH8bsfLSFqqJLdIcpPMgdimTZtgNBpRrVq1HJWJiPSBidtE5HAkb2j9+vU4f/48IiIi0kaoScAjidIyn9Hx48exZMkSq8TpjCR36ezZs6r1SLrbpNtt0aJFVseTLjt5XjlefHy81fNIa5TkPfXv3x8HDx5UidlDhw7Fk08+mdbVRkSOhUESETkcGdl2+vRpVKpUCcWLF1fb6tati3Xr1uHYsWNqGoAGDRpg9OjRCAkJyfK5HnzwQTWdgART9evXV4GWedSbmYyYk5Fz7du3V8ebN2+e1fPI9AF//vmnmvSySZMm6NOnD+677z6VpE1EjokzbhMRERHZwJYkIiIiIhsYJBERERHZwCCJiIiIyAYGSUREREQ2MEgiIiIisoFBEhEREZENDJKIiIiIbGCQRERERGQDgyQiIiIiGxgkEREREdnAIImIiIjIBgZJRERERLD2f1qCWQFT3G9LAAAAAElFTkSuQmCC", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "PyObject " + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "figure()\n", + "semilogy(e_fp, \".-\", label=\"fixed-point residual norm\")\n", + "semilogy(e_nt, \".-\", label=\"Newton residual norm\")\n", + "xlabel(\"iteration\"); ylabel(\"‖r(x_k)‖\"); title(\"Convergence per implicit step\"); grid(true); legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/class02/part2_eq_constraints.ipynb b/class02/part2_eq_constraints.ipynb new file mode 100644 index 0000000..8b994b3 --- /dev/null +++ b/class02/part2_eq_constraints.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m new project at `~/Desktop/Summer_2025/Opt-Control-Deza`\n" + ] + } + ], + "source": [ + "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using ForwardDiff\n", + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "∇2f (generic function with 1 method)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Q = Diagonal([0.5; 1])\n", + "function f(x)\n", + " return 0.5*(x-[1; 0])'*Q*(x-[1; 0])\n", + "end\n", + "function ∇f(x)\n", + " return Q*(x-[1; 0])\n", + "end\n", + "function ∇2f(x)\n", + " return Q\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "∂c (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function c(x)\n", + " return x[1]^2 + 2*x[1] - x[2]\n", + "end\n", + "function ∂c(x)\n", + " return [2*x[1]+2 -1]\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function plot_landscape()\n", + " Nsamp = 20\n", + " Xsamp = kron(ones(Nsamp),LinRange(-4,4,Nsamp)')\n", + " Ysamp = kron(ones(Nsamp)',LinRange(-4,4,Nsamp))\n", + " Zsamp = zeros(Nsamp,Nsamp)\n", + " for j = 1:Nsamp\n", + " for k = 1:Nsamp\n", + " Zsamp[j,k] = f([Xsamp[j,k]; Ysamp[j,k]])\n", + " end\n", + " end\n", + " contour(Xsamp,Ysamp,Zsamp)\n", + "\n", + " xc = LinRange(-3.2,1.2,Nsamp)\n", + " plot(xc,xc.^2+2.0.*xc,\"y\")\n", + "end\n", + "\n", + "plot_landscape()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "newton_step (generic function with 1 method)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function newton_step(x0,λ0)\n", + " H = ∇2f(x0) + ForwardDiff.jacobian(x -> ∂c(x)'*λ0, x0)\n", + " C = ∂c(x0)\n", + " Δz = [H C'; C 0]\\[-∇f(x0)-C'*λ0; -c(x0)]\n", + " Δx = Δz[1:2]\n", + " Δλ = Δz[3]\n", + " return x0+Δx, λ0+Δλ\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = [-1; -1]\n", + "λguess = [0.0]\n", + "plot_landscape()\n", + "plot(xguess[1], xguess[2], \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew, λnew = newton_step(xguess[:,end],λguess[end])\n", + "xguess = [xguess xnew]\n", + "λguess = [λguess λnew]\n", + "plot_landscape()\n", + "plot(xguess[1,:], xguess[2,:], \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2×2 Matrix{Float64}:\n", + " -1.5 0.0\n", + " 0.0 1.0" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H = ∇2f(xguess[:,end]) + ForwardDiff.jacobian(x -> ∂c(x)'*λguess[end], xguess[:,end])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2×2 Diagonal{Float64, Vector{Float64}}:\n", + " 0.5 ⋅ \n", + " ⋅ 1.0" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "∇2f(xguess[:,end])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "gauss_newton_step (generic function with 1 method)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function gauss_newton_step(x0,λ0)\n", + " H = ∇2f(x0)\n", + " C = ∂c(x0)\n", + " Δz = [H C'; C 0]\\[-∇f(x0)-C'*λ0; -c(x0)]\n", + " Δx = Δz[1:2]\n", + " Δλ = Δz[3]\n", + " return x0+Δx, λ0+Δλ\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = [-3; 2]\n", + "λguess = [0.0]\n", + "plot_landscape()\n", + "plot(xguess[1], xguess[2], \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xnew, λnew = gauss_newton_step(xguess[:,end],λguess[end])\n", + "xguess = [xguess xnew]\n", + "λguess = [λguess λnew]\n", + "plot_landscape()\n", + "plot(xguess[1,:], xguess[2,:], \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/class02/part3_ipm.ipynb b/class02/part3_ipm.ipynb new file mode 100644 index 0000000..8100f3a --- /dev/null +++ b/class02/part3_ipm.ipynb @@ -0,0 +1,639 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "012f9b4d-9754-467b-9b9c-7367f77ba292", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Desktop/Summer_2025/Opt-Control-Deza`\n" + ] + } + ], + "source": [ + "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d129e500-1db0-4f09-ba14-1c60d953792a", + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using ForwardDiff\n", + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "65202fb8-a805-4033-93c0-6a4cdf7810c9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "∇2f (generic function with 1 method)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Q = Diagonal([0.5; 1])\n", + "# Set up QP\n", + "function f(x)\n", + " return 0.5*(x-[1; 0])'*Q*(x-[1; 0])\n", + "end\n", + "function ∇f(x)\n", + " return Q*(x-[1; 0])\n", + "end\n", + "function ∇2f(x)\n", + " return Q\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "583fbdc4-375b-4013-8064-f00842c19240", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "∂c (generic function with 1 method)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = [-1.0 1.0]\n", + "b = 1.0\n", + "function c(x)\n", + " return dot(A,x) - b\n", + "end\n", + "function ∂c(x)\n", + " return A\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "732a988e-de84-47c6-a24e-c262f45f2896", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function plot_landscape()\n", + " Nsamp = 20\n", + " Xsamp = kron(ones(Nsamp),LinRange(-4,4,Nsamp)')\n", + " Ysamp = kron(ones(Nsamp)',LinRange(-4,4,Nsamp))\n", + " Zsamp = zeros(Nsamp,Nsamp)\n", + " for j = 1:Nsamp\n", + " for k = 1:Nsamp\n", + " Zsamp[j,k] = f([Xsamp[j,k]; Ysamp[j,k]])\n", + " end\n", + " end\n", + " contour(Xsamp,Ysamp,Zsamp)\n", + "\n", + " xc = LinRange(-4,3,Nsamp)\n", + " plot(xc,xc.+1,\"y\")\n", + "end\n", + "\n", + "# feasible region is defined by inequality constraint\n", + "plot_landscape()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "ef406b43-4ba2-4993-9761-b8aa631cc7d9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "ip_residual (generic function with 1 method)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The residual function; i.e the F.O.N.C that needs to be zero\n", + "function ip_residual(z, ρ)\n", + " x = z[1:2]\n", + " σ = z[3]\n", + " r = [∇f(x) - ∂c(x)'*sqrt(ρ)*exp(-σ);\n", + " c(x) - sqrt(ρ)exp(σ)]\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "309697fc-2a04-47fb-b590-3062a538fd4a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "kkt_residual (generic function with 1 method)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# this is the actual true stock KKT system\n", + "function kkt_residual(z)\n", + " x = z[1:2]\n", + " σ = z[3]\n", + " λ = sqrt(ρ)*exp(-σ)\n", + "\n", + " r = [∇f(x) - ∂c(x)'*λ;\n", + " min(λ, 0)\n", + " min(c(x),0)\n", + " λ*c(x)]\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "9435f612-6482-4015-9d48-c2e68217a2ef", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xguess = [-2; 2] # we are in the interior\n", + "σguess = 0.0\n", + "z = [xguess; σguess]\n", + "plot_landscape()\n", + "plot(z[1], z[2], \"rx\")" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "16393539-1f14-4703-b938-1423bd5d9de1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3×1 Matrix{Float64}:\n", + " -0.5\n", + " 1.0\n", + " 2.0" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ρ = 1.0\n", + "ip_residual(z,ρ)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "0dd9b9d0-5615-4459-b420-7dba9e9a83ca", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5×1 Matrix{Float64}:\n", + " -0.5\n", + " 1.0\n", + " 0.0\n", + " 0.0\n", + " 3.0" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kkt_residual(z)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "49c45196-d8ce-4ac5-86d3-192e33ec655a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "newton_solve (generic function with 1 method)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function newton_solve(z0,ρ,tol)\n", + "\n", + " #initial guess\n", + " z = z0\n", + " \n", + " #KKT residual\n", + " r = ip_residual(z,ρ)\n", + "\n", + " # while not converged\n", + " while norm(r) > tol \n", + " #H = ∇2f(x)\n", + " #C = ∂c(x)\n", + "\n", + " #M = [H sqrt(ρ)*C'*exp(-σ);\n", + " # C -sqrt(ρ)*exp(σ)]\n", + "\n", + " #Newton step: evaluate jacobian of residal\n", + " M = ForwardDiff.jacobian(dz->ip_residual(dz,ρ), z)\n", + " Δz = -M\\r\n", + "\n", + " znew = z + Δz\n", + " rnew = ip_residual(znew,ρ)\n", + "\n", + " #Line search with armijo\n", + " b = 0.1\n", + " c = 0.5\n", + " α = 1.0\n", + " while norm(rnew) > (norm(r) + b*α*dot(r,M*Δz)/norm(r))\n", + " α = c*α\n", + " znew = z + α*Δz\n", + " rnew = ip_residual(znew,ρ)\n", + " end\n", + "\n", + " z = znew\n", + " r = rnew\n", + " end\n", + "\n", + " return z\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "2effd81a-aee6-48bc-b692-8c1ebb992195", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -2.0\n", + " 2.0\n", + " 0.0" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "z_iter = z" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "c1129f5c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3×2 Matrix{Float64}:\n", + " -2.0 -1.0\n", + " 2.0 1.0\n", + " 0.0 0.0" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ρ = 1.0 \n", + "z = newton_solve(z_iter[:,end],ρ,1e-10) # a relaxed solution\n", + "z_iter = [z_iter z]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "b7053708", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5×1 Matrix{Float64}:\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 0.0\n", + " 1.0" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kkt_residual(z)\n", + "# super cool, basically the residual error's are zero everywhere except the complementarity as that is what we relaxed" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "fa579422", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3×1 Matrix{Float64}:\n", + " 0.0\n", + " 0.0\n", + " 0.0" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ip_residual(z,ρ)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "6ede962b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_landscape()\n", + "plot(z_iter[1,:], z_iter[2,:], \"rx\") # Need to keep on driving rho down closer to 0 to approach constraint" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "b51486c0-a9cd-4a12-a846-32f57fd32c41", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3×3 Matrix{Float64}:\n", + " -2.0 -1.0 -0.333333\n", + " 2.0 1.0 0.666667\n", + " 0.0 0.0 -8.80488" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ρ = 1.0e-8 #adjust from ρ=1 to ρ=1e-8 to observe convergence along central path. Warm start with prior iter\n", + "z = newton_solve(z_iter[:,end],ρ,1e-10)\n", + "z_iter = [z_iter z]" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "b3ae1497-dd3f-41e2-bfa6-613e38f08ebc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5×1 Matrix{Float64}:\n", + " 2.8343993818680246e-13\n", + " -2.8343993818680246e-13\n", + " 0.0\n", + " 0.0\n", + " 1.000000001422954e-8" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kkt_residual(z) # amazing, super close to now satisfying the original kkt conditions" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "52d70903-e6dd-47ad-9d46-d88e4f5dc39c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Vector{PyCall.PyObject}:\n", + " PyObject " + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_landscape()\n", + "plot(z_iter[1,:], z_iter[2,:], \"rx\")\n", + "# the path that the solution follows as you crank rho down is called the \"central path\"" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f1a996bb-9fb5-4419-bfe3-026fafc767b8", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3×3 Matrix{Float64}:\n", + " 0.5 0.0 -0.666667\n", + " 0.0 1.0 0.666667\n", + " -1.0 1.0 -1.5e-8" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M = ForwardDiff.jacobian(dz->ip_residual(dz,ρ), z)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "12bb1ec7-945d-4ae7-a37a-dc30db289636", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Vector{Float64}:\n", + " -0.8526850467837964\n", + " 0.7169780264777998\n", + " 1.6357070053059972" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "eigvals(M)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "774f83a1-6eb2-4e04-8047-8021b158a9e9", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From a78fc9d51aed7e5522eb4e98db5023ef58106b84 Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Fri, 29 Aug 2025 11:52:54 -0400 Subject: [PATCH 3/8] updated notes --- 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b/class02/eq_constraints.tex @@ -5,7 +5,7 @@ \section{Constrained Optimization} % ==== Equality constraints: KKT, Newton vs. Gauss–Newton ==== \begin{frame}{Equality-constrained minimization: geometry and conditions} -\textbf{Problem.}; $\min_{x\in\mathbb{R}^n} f(x)\quad \text{s.t.}\quad C(x)=0, C:\mathbb{R}^n\to\mathbb{R}^m$. +\textbf{Problem}; $\min_{x\in\mathbb{R}^n} f(x)\quad \text{s.t.}\quad C(x)=0, C:\mathbb{R}^n\to\mathbb{R}^m$. \medskip \textbf{Geometric picture.} At an optimum on the manifold $C(x)=0$, the negative gradient must lie in the tangent space: @@ -33,6 +33,38 @@ \section{Constrained Optimization} +\section{Constrained Optimization} + +% ==== Slide 1: Picture-first intuition ==== +\begin{frame}[t]{Equality constraints: picture first} +\setbeamercovered{invisible} + +\textbf{Goal.} Minimize $f(x)$ while staying on the surface $C(x)=0$. + +\uncover<2->{\textbf{Feasible set as a surface.} Think of $C(x)=0$ as a smooth surface embedded in $\mathbb{R}^n$ (a manifold).} + +\uncover<3->{\textbf{Move without breaking the constraint.} Tangent directions are the “along-the-surface” moves that keep $C(x)$ unchanged to first order. Intuitively: tiny steps that slide on the surface.} + +\uncover<4->{\textbf{What must be true at the best point.} At $x^\star$, there is no downhill direction that stays on the surface. Equivalently, the usual gradient of $f$ has \emph{no component along the surface}.} + +\uncover<5->{\textbf{Normals enter the story.} If the gradient can’t point along the surface, it must point \emph{through} it—i.e., it aligns with a combination of the surface’s normal directions (one normal per constraint).} +\end{frame} + +% ==== Slide 2: From picture to KKT ==== +\begin{frame}[t]{From the picture to KKT (equality case)} +\setbeamercovered{invisible} + +\textbf{KKT conditions at a regular local minimum (equality only):} + +\uncover<1->{\textbf{1) Feasibility:} $C(x^\star)=0$. \emph{(We’re on the surface.)}} + +\uncover<2->{\textbf{2) Stationarity:} $\nabla f(x^\star) + J_C(x^\star)^{\!T}\lambda^\star = 0$. \emph{(The gradient is a linear combination of the constraint normals.)}} + +\uncover<3->{\textbf{Lagrangian viewpoint.} Define $L(x,\lambda)=f(x)+\lambda^{\!T}C(x)$. At a solution, $x^\star$ is a stationary point of $L$ w.r.t.\ $x$ (that’s the stationarity equation), while $C(x^\star)=0$ enforces feasibility.} + +\uncover<4->{\textbf{What the multipliers mean.} The vector $\lambda^\star$ tells how strongly each constraint “pushes back” at the optimum; it also measures sensitivity of the optimal value to small changes in the constraints.} + +\end{frame} \begin{frame}{KKT system for equalities (first-order necessary conditions)} @@ -57,9 +89,12 @@ \section{Constrained Optimization} $$ \textit{Notes.} This is a symmetric \emph{saddle-point} system; typical solves use block elimination (Schur complement) or sparse factorizations. +\end{frame} + + + -\end{frame} \begin{frame}{Move to Julia Code} \begin{center} @@ -68,42 +103,55 @@ \section{Constrained Optimization} \end{frame} \begin{frame}{Numerical practice: Newton on KKT} -\textbf{When it works best.} -\begin{itemize} -\item Near a regular solution with $J_{C}(x^\star)$ full row rank and positive-definite reduced Hessian. -\item With a globalization (line search on a merit function) and mild regularization for robustness. -\end{itemize} - -\textbf{Common safeguards.} -\begin{itemize} -\item \emph{Regularize} the $(1,1)$ block to ensure a good search direction (e.g., add $\beta I$). -\item \emph{Merit/penalty} line search to balance feasibility vs.\ optimality during updates. -\item \emph{Scaling} constraints to improve conditioning of the KKT system. -\end{itemize} + \setbeamercovered{invisible} + + + \textbf{When it works best.} + \begin{itemize} + \item Near a regular solution with $J_{C}(x^\star)$ full row rank and positive-definite reduced Hessian. + \item With a globalization (line search on a merit function) and mild regularization for robustness. + \end{itemize} + + % --- Part 2: appears on the 2nd click only --- + \uncover<2->{% + \textbf{Common safeguards.} + \begin{itemize} + \item \emph{Regularize} the $(1,1)$ block to ensure a good search direction (e.g., add $\beta I$). + \item \emph{Merit/penalty} line search to balance feasibility vs.\ optimality during updates. + \item \emph{Scaling} constraints to improve conditioning of the KKT system. + \end{itemize} + } +\end{frame} -\end{frame} +\begin{frame}{Gauss--Newton vs. full Newton on KKT} -\begin{frame}{Gauss--Newton vs.\ full Newton on KKT} -\textbf{Full Newton Hessian of the Lagrangian:} $\nabla_{xx}^2 L(x,\lambda) &= \hess f(x)+\sum_{i=1}^m \lambda_i\,\hess C_i(x)$ +\uncover<1->{ +\textbf{Full Newton Hessian of the Lagrangian:}\quad +$\nabla_{xx}^2 L(x,\lambda) = \nabla^2 f(x) + \sum_{i=1}^m \lambda_i\, \nabla^2 C_i(x)$ +} -\textbf{Gauss--Newton approximation:} drop the \emph{constraint-curvature} term $\sum_i \lambda_i,\hess C_i(x)$: +\vspace{0.6em} -\begin{align*} -H_{\text{GN}}(x) &\approx \hess f(x). +\uncover<2->{ +\textbf{Gauss--Newton approximation:} drop the \emph{constraint-curvature} term +$\sum_{i=1}^m \lambda_i\, \nabla^2 C_i(x)$: +\begin{align*} +H_{\text{GN}}(x) &\approx \nabla^2 f(x). \end{align*} +} +\uncover<3->{ \textbf{Trade-offs (high level).} \begin{itemize} -\item \emph{Full Newton:} fewer iterations near the solution, but each step is costlier and can be less robust far from it. -\item \emph{Gauss--Newton:} cheaper per step and often more stable; may need more iterations but wins in wall-clock on many problems. + \item \emph{Full Newton:} fewer iterations near the solution, but each step is costlier and can be less robust far from it. + \item \emph{Gauss--Newton:} cheaper per step and often more stable; may need more iterations but wins in wall-clock on many problems. \end{itemize} - -\textbf{Practice tip.} Start with GN (with line search); switch to full Newton (or add low-rank updates) as feasibility improves. - +} \end{frame} + % ==== Inequalities & KKT: complementarity ==== \begin{frame}{Inequality-constrained minimization and KKT} diff --git a/class02/figures/log_barrier.png b/class02/figures/log_barrier.png new file mode 100644 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z|BDsd9)oUFe52-DbCKc8VpXq4$_lsN>SMgBR&o%7uF`PTi1}KelKL>t6g+)_M#^f^ zqt#TG^*0BdicHO3m=pPB`@s7L)ZPSZXb)qx%`_i7wpJl=1#+J8=RR8XBWA=y3~BSP zA&>rh$Q<2^1g7*PM5}NltBV_BIJb+B7h%@wJ++-Ze7uv?+rRshxhUYI&e0$; minimize the penalized unconstrained objective. \item Increase $\rho$ (e.g., $\times 10$) and warm start from previous $x$. \item Stop when $c^-(x)$ is small enough. \end{enumerate} +\end{frame} + +% --- Slide 3: Quadratic penalty & why large $\rho$ is needed ---------------- +\begin{frame}{Quadratic penalty: need large $\rho$ for strong feasibility pressure} +\begin{columns}[T,onlytextwidth] +\column{0.45\textwidth} +\small \textbf{Pros.} Dead simple; reuse unconstrained machinery (Grad/Newton + line search). \\ -\textbf{Cons.} Ill-conditioning as $\rho\to\infty$ to satisfy constraints.; struggles to reach high accuracy; multipliers are implicit. \\ -\textbf{Popular fix}: estimate $\lambda$ from penalty at each iteration to be able to converge with finite $\rho$. Called “Augmented Lagrangian” (also closely related to ADMM). +\textbf{Cons.} Ill-conditioning as $\rho\to\infty$; struggles to reach high accuracy; multipliers are implicit. \\ +\textbf{Popular fix.} Estimate $\lambda$ (Augmented Lagrangian / ADMM) to converge with finite $\rho$. + +\vspace{0.6em} +\textbf{Takeaway.} The penalty outside the feasible set ($x<0$ here) is only quadratic, +so to make violations tiny you often must crank $\rho$ very large $\Rightarrow$ poor conditioning. + +\column{0.53\textwidth} +\centering +\includegraphics[width=\textwidth]{figures/quadratic_penalty.png} +\end{columns} \end{frame} @@ -77,28 +95,36 @@ \section{Minimization w/ Inequality Constraints} -% ---- ALM ---- -\begin{frame}{Augmented Lagrangian (ALM): fix penalty’s weaknesses} -\textbf{Core idea.} Introduce multipliers $\lambda$ so we can keep $\rho$ moderate and still achieve accuracy. -\textbf{Lagrangian for equality case:} $\mathcal{L}_\rho(x,\lambda)=f(x)+\lambda^{\!T}C(x)+\tfrac{\rho}{2}\|C(x)\|_2^2.$ +% ---- ALM ---- +\begin{frame}[t]{Augmented Lagrangian (ALM): fix penalty’s weaknesses} +\setbeamercovered{invisible} -\textbf{Outer loop.} +\uncover<1->{\textbf{Core idea.}\; Introduce multipliers $\lambda$ so we can keep $\rho$ moderate and still achieve accuracy.} + +\uncover<2->{\textbf{Lagrangian for equality case:}\; +$\displaystyle \mathcal{L}_\rho(x,\lambda)=f(x)+\lambda^{\!T}C(x)+\tfrac{\rho}{2}\|C(x)\|_2^2.$} + +\uncover<3->{\textbf{Outer loop.} \begin{enumerate} -\item $x^{k+1}\approx \arg\min_x \mathcal{L}_\rho(x,\lambda^k)$ (unconstrained solve). -\item $\lambda^{k+1}=\lambda^k+\rho\,C(x^{k+1})$. + \item $x^{k+1}\approx \arg\min_x \mathcal{L}_\rho(x,\lambda^k)$ (unconstrained solve). + \item $\lambda^{k+1}=\lambda^k+\rho\,C(x^{k+1})$. \end{enumerate} - -\textbf{Inequalities (sketch).} Apply to the \emph{hinge} $c^-(x)$ and keep $\lambda\ge 0$: - -$$ +} + +\uncover<4->{\textbf{Inequalities (sketch).}\; Apply to the \emph{hinge} $c^-(x)$ and keep $\lambda\ge 0$: +\[ \mathcal{L}_\rho(x,\lambda)=f(x)-\lambda^{\!T}c(x)+\tfrac{\rho}{2}\|c^-(x)\|_2^2,\quad \lambda^{k+1}=\max\!\big(0,\lambda^k-\rho\,c(x^{k+1})\big). -$$ +\] +} -\textbf{Why it works.} Subproblems are better conditioned than pure penalty; $\lambda$ estimates improve the model; finite $\rho$ can reach high accuracy. +\uncover<5->{\textbf{Why it works.}\; Subproblems are better conditioned than pure penalty; $\lambda$ estimates improve the model; finite $\rho$ can reach high accuracy.} \end{frame} + + + \begin{frame}{ALM in practice (optimization loop view)} \textbf{Inner solver.} Use (damped) Newton or quasi-Newton on $\mathcal{L}_\rho(\cdot,\lambda^k)$ with Armijo/Wolfe line search. \\ \textbf{Tuning.} @@ -109,7 +135,7 @@ \section{Minimization w/ Inequality Constraints} \textbf{When to pick ALM.} \begin{itemize} \item Nonconvex NLPs where feasibility progress matters and you want robust globalization. -\item Medium accuracy is fine, or as a precursor to a polished PDIP phase on a convex QP. +\item When medium accuracy is tolerable/fine, or as a precursor to a polished PDIP phase on a convex QP. \end{itemize} \end{frame} @@ -123,7 +149,7 @@ \section{Minimization w/ Inequality Constraints} \begin{frame}{Interior-Point / Barrier Methods} -Replace inequalities with barrier function in objective: +\underline{\textbf{TLDR: }} Replace inequalities with barrier function in objective: $$ \min f(x), \quad x \geq 0 \quad \to \quad \min f(x) - \rho \log(x) @@ -134,9 +160,18 @@ \section{Minimization w/ Inequality Constraints} \item Fast convergence with Newton and strong theoretical properties. \item Used in IPOPT. \end{itemize} +\end{frame} -(Diagram: $-\log(x)$ barrier.) - + +% --- Slide 2: Barrier intuition (contrast) --------------------------------- +\begin{frame}{Barrier intuition issue: $-\log(x)$ blows up near the boundary} +\centering +\includegraphics[scale=0.5]{figures/log_barrier.png} + +{\small +For an inequality like $x\ge 0$, the log barrier $-\log(x)$ goes to $\infty$ as $x\to 0^+$, +creating a \emph{hard wall} at the boundary (contrast with quadratic penalties). +} \end{frame} @@ -182,6 +217,12 @@ \section{Minimization w/ Inequality Constraints} \end{frame} +\begin{frame}{Log-Domain Interior-Point Method} +\begin{center} + \includegraphics[scale=0.4]{figures/tri_paper.png} +\end{center} +\end{frame} + \begin{frame}{Log-Domain Interior-Point Method} \textbf{More general constraint case}: \quad \quad \quad \quad \quad $\min f(x) \quad \text{s.t. } c(x) \geq 0$ @@ -220,10 +261,79 @@ \section{Minimization w/ Inequality Constraints} \end{frame} + + + + +\begin{frame}{Log-Domain Interior-Point Method} + +\textbf{Change of variables (elementwise):} +\[ +\boxed{\ \rho := s \circ \lambda,\qquad +\sigma := \tfrac{1}{2}\big(\log s - \log \lambda\big)\ } +\quad\Longleftrightarrow\quad +\boxed{\ s = \sqrt{\rho}\, \circ e^{\sigma},\quad +\lambda = \sqrt{\rho}\, \circ e^{-\sigma}\ } +\] +{\footnotesize +Here \(\circ\) is the Hadamard (elementwise) product; \(s,\lambda,\rho,\sigma\in\mathbb{R}^m\) with \(s>0,\lambda>0\). +By construction \(s\ge 0,\ \lambda\ge 0\) and \(\rho = s\circ\lambda\) (the relaxed complementarity) holds.} + +\vspace{0.6em} + +\textbf{KKT (first-order) residuals with inequality \(c(x) - s = 0\):} +\[ +r_x(x,\sigma) := \nabla f(x) - J(x)^{\!T}\lambda(\sigma), +\qquad +r_c(x,\sigma) := c(x) - s(\sigma) = 0, +\] +where \(J(x) := \frac{\partial c}{\partial x}(x)\), +\(s(\sigma)=\sqrt{\rho}\circ e^{\sigma}\), +\(\lambda(\sigma)=\sqrt{\rho}\circ e^{-\sigma}\). + +\end{frame} + \begin{frame}{Log-Domain Interior-Point Method} + +\textbf{(Gauss-)Newton step in \((x,\sigma)\) for fixed \(\rho\):} +\[ +\begin{bmatrix} +H & J^{\!T}\Lambda \\[2pt] +J & -S +\end{bmatrix} +\begin{bmatrix} +\delta x \\ \delta \sigma +\end{bmatrix} += +- +\begin{bmatrix} +r_x \\ r_c +\end{bmatrix} +\quad\text{with}\quad +S:=\operatorname{diag}(s),\ \Lambda:=\operatorname{diag}(\lambda). +\] +{\footnotesize +Here \(H\) is your Hessian model w.r.t.\ \(x\): +\( +H=\nabla^2 f(x)\ \) (Gauss--Newton/curvature-drop), +or +\( +H=\nabla^2 f(x)-\sum_{i=1}^m \lambda_i \nabla^2 c_i(x) +\) (full Newton). +Note the simple sensitivities: +\(ds = S\,d\sigma,\ d\lambda = -\Lambda\,d\sigma\), +which produce the block entries \(-S\) and \(J^{\!T}\Lambda\). +} + +\end{frame} + + + + +\begin{frame}{Log-Domain Interior-Point Method (easier notation)} \textbf{To ensure $s \geq 0$ and $\lambda \geq 0$, introduce change of variables:} $$s = \sqrt{\rho} e^{\sigma}, \quad \lambda = \sqrt{\rho} e^{-\sigma}$$ -Now (relaxed) complementarity is always satisfied by construction. +Now (relaxed) complementarity is \textbf{always satisfied} by construction! Plug back into F.O.N.C @@ -252,6 +362,10 @@ \section{Minimization w/ Inequality Constraints} \end{frame} + + + + \begin{frame}{Example: Quadratic Program} Super common problem to be solved in control applications: quadratic programs $$ @@ -279,25 +393,27 @@ \section{Minimization w/ Inequality Constraints} \end{frame} -% ---- Comparison ---- +% ---- Comparison (animated main bullets) ---- \begin{frame}{Penalty vs.\ ALM vs.\ PDIP: what changes?} \begin{itemize} -\item \textbf{Feasibility handling:} -\begin{itemize} -\item Penalty: encourages $c(x)\ge 0$ via cost; feasibility only in the limit $\rho\uparrow$. -\item ALM: balances optimality and feasibility via $\lambda$ updates at finite $\rho$. -\item PDIP: enforces strict interior $c(x)>0$; drives $s_i\lambda_i=\rho\to 0$. -\end{itemize} -\item \textbf{Conditioning:} -\begin{itemize} -\item Penalty gets ill-conditioned as $\rho$ grows. -\item ALM keeps conditioning reasonable. -\item PDIP maintains well-scaled Newton systems near the path (with proper scaling). + \item<1-> \textbf{Feasibility handling:} + \begin{itemize} + \item Penalty: encourages $c(x)\ge 0$ via cost; feasibility only in the limit $\rho\uparrow$. + \item ALM: balances optimality and feasibility via $\lambda$ updates at finite $\rho$. + \item PDIP: enforces strict interior $c(x)>0$; drives $s_i\lambda_i=\rho\to 0$. + \end{itemize} + + \item<2-> \textbf{Conditioning:} + \begin{itemize} + \item Penalty gets ill-conditioned as $\rho$ grows. + \item ALM keeps conditioning reasonable. + \item PDIP maintains well-scaled Newton systems near the path (with proper scaling). + \end{itemize} + + \item<3-> \textbf{Accuracy:} Penalty (low–med), ALM (high with finite $\rho$), PDIP (high; excellent for convex). + + \item<4-> \textbf{Per-iteration work:} Penalty/ALM solve unconstrained-like subproblems; PDIP solves structured KKT systems with slacks/duals. \end{itemize} -\item \textbf{Accuracy:} Penalty (low–med), ALM (high with finite $\rho$), PDIP (high; excellent for convex). -\item \textbf{Per-iteration work:} Penalty/ALM solve unconstrained-like subproblems; PDIP solves structured KKT systems with slacks/duals. -\end{itemize} - \end{frame} - + \ No newline at end of file diff --git a/class02/intro.tex b/class02/intro.tex index 2313f3f..8b4f0c8 100644 --- a/class02/intro.tex +++ b/class02/intro.tex @@ -10,7 +10,7 @@ \section{Overview and Big Picture of Lecture 2} \textbf{Goals for today} \begin{itemize} \item Pick and configure an optimizer for small control problems (unconstrained \& constrained). -\item Derive KKT conditions and form the SQP QP subproblem for a nonlinear program. +\item Derive KKT conditions and form the SQP/QP subproblems for a nonlinear program. \item Explain the differences between penalty, augmented Lagrangian, and interior-point methods. \end{itemize} \textbf{Why?}\\ @@ -22,7 +22,7 @@ \section{Overview and Big Picture of Lecture 2} \begin{enumerate} \item Big picture and some notation \hfill \textit{(5 min)} \item Unconstrained optimization: Root-finding, Newton and globalization \hfill \textit{(30 min)} -\item Equality constraints: KKT, Newton vs. Gauss–Newton \hfill \textit{(20 min)} +\item Equality constraints: KKT, Newton vs. Gauss–Newton \hfill \textit{(30 min)} \item Inequalities \& KKT: complementarity \hfill \textit{(10 min)} \item Methods: penalty $\rightarrow$ ALM $\rightarrow$ interior-point (PDIP) \hfill \textit{(20 min)} \item Brief look at SQP for solving hard control problems \hfill \textit{(20 min)} diff --git a/class02/notation.tex b/class02/notation.tex index d38fcd9..9f93367 100644 --- a/class02/notation.tex +++ b/class02/notation.tex @@ -1,33 +1,117 @@ -\begin{frame}{Some Notation:} -Given $f(x): \mathbb{R}^n \to \mathbb{R}$ \quad \quad \quad \quad \quad \quad \quad \quad $\frac{\partial f}{\partial x} \in \mathbb{R}^{1 \times n} \quad \text{is a row vector}$ +% ===== Slide 1: Derivatives & Jacobians (animated in 4 parts) ===== +\begin{frame}{Notation I: derivatives \& Jacobians} -This is because $\frac{\partial f}{\partial x}$ is the linear operator mapping $\Delta x$ into $\Delta f$: +\begin{columns}[T,onlytextwidth] +\column{0.52\textwidth} +\uncover<1->{ +\begin{block}{Scalar-valued function} +$f:\mathbb{R}^n \to \mathbb{R}$ -$$ -f(x + \Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x -$$ +\vspace{0.2em} +Row-derivative (row gradient): +\[ +\frac{\partial f}{\partial x} \in \mathbb{R}^{1\times n} +\] +\end{block} +} -Similarly $g(y): \mathbb{R}^m \to \mathbb{R}^n$ \quad \quad \quad \quad \quad $\frac{\partial g}{\partial y} \in \mathbb{R}^{n \times m} \quad \text{because}$ +\uncover<2->{ +\begin{block}{First-order model of $f$} +\[ +f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\,\Delta x +\] +\[ +\Delta x \in \mathbb{R}^n,\quad \frac{\partial f}{\partial x}\in\mathbb{R}^{1\times n},\quad +\Delta f\in\mathbb{R} +\] +\end{block} +} + +\column{0.48\textwidth} +\uncover<3->{ +\begin{block}{Vector-valued function} +$g:\mathbb{R}^m \to \mathbb{R}^n$ + +\vspace{0.2em} +Jacobian: +\[ +\frac{\partial g}{\partial y} \in \mathbb{R}^{n\times m} +\] +\end{block} +} + +\uncover<4->{ +\begin{block}{First-order model of $g$} +\[ +g(y+\Delta y) \approx g(y) + \frac{\partial g}{\partial y}\,\Delta y +\] +\[ +\Delta y\in\mathbb{R}^m,\quad \frac{\partial g}{\partial y}\in\mathbb{R}^{n\times m},\quad +\Delta g\in\mathbb{R}^n +\] +\end{block} +} +\end{columns} -$$ -g(y+\Delta y) \approx g(y) + \frac{\partial g}{\partial y}\Delta y -$$ \end{frame} -\begin{frame}{Some notation:} -For convenience, we will define: -$$ -\nabla f(x) = \left(\frac{\partial f}{\partial x}\right)^T \in \mathbb{R}^n \quad \text{(column vector)} -$$ +% ==== Slide 2 (fits on one page, animated in 4 parts) ==== +\begin{frame}{Notation II: gradient, Hessian \& Taylor} +\begingroup +\small +% tighten display math spacing just for this frame +\setlength{\abovedisplayskip}{6pt} +\setlength{\belowdisplayskip}{6pt} +\setlength{\abovedisplayshortskip}{4pt} +\setlength{\belowdisplayshortskip}{4pt} + +\begin{columns}[T,onlytextwidth] + \column{0.48\textwidth} + \uncover<1->{ + \begin{block}{Gradient (column form)} + For $f:\mathbb{R}^n\to\mathbb{R}$, + \[ + \nabla f(x) := \left(\frac{\partial f}{\partial x}\right)^{\!T} \in \mathbb{R}^{n} + \] + \end{block} + } -$$ -\nabla^2 f(x) = \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial x}\right) = \frac{\partial^2 f}{\partial x^2} \in \mathbb{R}^{n \times n} -$$ + \uncover<2->{ + \begin{block}{Hessian} + \[ + \nabla^2 f(x) := \frac{\partial}{\partial x}\!\left(\frac{\partial f}{\partial x}\right) + = \frac{\partial^2 f}{\partial x^2} \in \mathbb{R}^{n\times n} + \] + \end{block} + } -$$ -f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x + \tfrac{1}{2}\Delta x^T \nabla^2 f(x)\Delta x -$$ - + \column{0.52\textwidth} + \uncover<3->{ + \begin{block}{Shape check} + \[ + \nabla f(x)\in\mathbb{R}^{n},\quad + \nabla^2 f(x)\in\mathbb{R}^{n\times n},\quad + \Delta x\in\mathbb{R}^{n} + \] + \[ + \Delta x^{\!T}\nabla^2 f(x)\Delta x \in \mathbb{R} + \] + \end{block} + } + + \uncover<4->{ + \begin{block}{Second-order Taylor} + \[ + f(x+\Delta x)\approx f(x) + + \nabla f(x)^{\!T}\Delta x + + \tfrac{1}{2}\,\Delta x^{\!T}\nabla^2 f(x)\,\Delta x + \] + \end{block} + } +\end{columns} +\endgroup \end{frame} + + diff --git a/class02/root_finding.tex b/class02/root_finding.tex index ae47f23..c72fe70 100644 --- a/class02/root_finding.tex +++ b/class02/root_finding.tex @@ -1,44 +1,102 @@ \section{Root-Finding} + -\begin{frame}{Root Finding} -Given $f(x)$, find $x^*$ such that $f(x^*) = 0$ (example: finding equilibrium of a continuous-time dynamics). +% Slide 1 — Big picture +\begin{frame}{Root-Finding and Fixed Points (Big Picture)} +\begin{itemize}\setlength\itemsep{0.6em} + \item \textbf{Root-finding:} given $f:\mathbb{R}^n\!\to\!\mathbb{R}^n$, find $x^\star$ with $f(x^\star)=0$ (e.g., steady states, nonlinear equations). + \item \textbf{Fixed point:} $x^\star$ is a fixed point of $g$ if $g(x^\star)=x^\star$ (discrete-time equilibrium). + \item \textbf{Bridge:} pick $g(x)=x-\alpha f(x)$ ($\alpha>0$) so that + \[ + f(x^\star)=0 \iff g(x^\star)=x^\star. + \] + \item \textbf{Mindset:} start $x_0$ and iterate $x_{k+1}=g(x_k)$ until nothing changes. +\end{itemize} +\end{frame} -Closely related: fixed point \quad \quad \quad $f(x^*) = x^* \quad (\text{equilibrium of discrete-time dynamics})$ +% Slide 2 — Convergence intuition +\begin{frame}{When Does Fixed-Point Iteration Converge?} +\begin{itemize}\setlength\itemsep{0.6em} + \item Near $x^\star$, $g$ behaves like its Jacobian $J_g(x^\star)$ (linearization). + \item \textbf{Contraction test:} scalar: $|g'(x^\star)|<1$; vector: spectral radius $\rho(J_g(x^\star))<1$. + \item Smaller contraction $\Rightarrow$ faster (linear) convergence; $\ge 1 \Rightarrow$ divergence/oscillations. + \item Converges only from within the \emph{basin of attraction} (good initial guess matters). +\end{itemize} +\end{frame} -\textbf{Fixed-Point Iteration} -\begin{itemize} - \item Simplest solution method - \item If fixed point is stable, just “iterate the dynamics” until it converges - \item Only works if $x^*$ is a stable equilibrium point and if initial guess is in the basin of attraction - \item can converge slowly (depends on $f$ i.e depending on eigenvalues) +% Slide 3 — Minimal recipe & stopping +\begin{frame}{Fixed-Point Iteration: Minimal Recipe} +\begin{itemize}\setlength\itemsep{0.6em} + \item Choose $g$ (often $g(x)=x-\alpha f(x)$) and an initial guess $x_0$. + \item Loop: \quad $x_{k+1}\leftarrow g(x_k)$. + \item Stop when residual $\|f(x_{k+1})\|$ is small, or step $\|x_{k+1}-x_k\|$ is small, or max iterations reached. + \item Report both: residual and step size (helps diagnose false convergence). +\end{itemize} +\end{frame} + +% Slide 4 — Tuning & practical tips +\begin{frame}{Tuning and Practical Tips} +\begin{itemize}\setlength\itemsep{0.6em} + \item \textbf{Step size $\alpha$:} too small $\Rightarrow$ slow; too large $\Rightarrow$ divergence/oscillation. Start modest; adjust cautiously. + \item \textbf{Damping:} $x_{k+1}\!\leftarrow\! (1-\beta)x_k+\beta g(x_k)$ with $0<\beta\le 1$ to stabilize. + \item \textbf{If stalled:} try a better $g$ (rescale/precondition $f$) or a better initial guess. + \item \textbf{Optimization link:} gradient descent is FPI on $\nabla F$: $g(x)=x-\eta\nabla F(x)$ solves $\nabla F(x^\star)=0$. + \item \textbf{When too slow:} use (quasi-)Newton methods for faster local convergence (needs derivatives/linear solves). \end{itemize} -Gradient Descent in Fixed Point Iteration applied to gradient of function $f$. \end{frame} + + + + +% ---- Newton's Method (animated in 4 parts) ---- \begin{frame}{Newton's Method} -TLDR: Instead os solving for $f(x) =0$, solve a linear for a linear approximation of $f(x)$.\\ -Fit a linear approximation to $f(x)$:\quad $f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\Delta x$ -Set approximation to zero and solve for $\Delta x$: +\uncover<1->{ +\underline{\textbf{TLDR}}: Instead of solving for $f(x)=0$, solve a linear system from a linear approximation of $f(x)$. +} -$$ -f(x) + \frac{\partial f}{\partial x}\Delta x = 0 \quad \Rightarrow \quad \Delta x = -\left(\frac{\partial f}{\partial x}\right)^{-1} f(x) -$$ +\vspace{0.6em} + +\uncover<2->{ +Fit a linear approximation to $f(x)$:\quad +$f(x+\Delta x) \approx f(x) + \frac{\partial f}{\partial x}\,\Delta x$ +} + +\vspace{0.6em} + +\uncover<3->{ +Set the approximation to zero and solve for $\Delta x$: +\[ +f(x) + \frac{\partial f}{\partial x}\,\Delta x = 0 +\quad \Rightarrow \quad +\Delta x = -\left(\frac{\partial f}{\partial x}\right)^{-1} f(x) +\] +} -Apply correction: $x \leftarrow x + \Delta x$ -Do this in a loop and repeat until convergence. +\vspace{0.6em} + +\uncover<4->{ +Apply the correction and iterate: +\[ +x \leftarrow x + \Delta x +\] +\smallskip +Repeat until convergence. +} \end{frame} + \begin{frame}{Example: Backward Euler} Last time: Implicit dynamics model (nonlinear function of current state and future state) $$ f(x_{n+1}, x_n, u_n) = 0 $$ -Implicit Euler: this time we have $x_{n+1}$ on the right; i.e evaluate f at future time. +Implicit Euler: this time we have $x_{n+1}$ on the right; i.e evaluate $f$ at future time. $$ x_{n+1} = x_n + h f(x_{n+1}) $$ @@ -64,29 +122,33 @@ \section{Root-Finding} \end{frame} -\begin{frame}{Minimization} -$$ -\min_x f(x), \quad f(x): \mathbb{R}^n \to \mathbb{R} -$$ -If $f$ is smooth, $\frac{\partial f}{\partial x}(x^*) = 0$ at a local minimum. - +\begin{frame}[t]{Minimization} +\[ +\min_x f(x), \quad f:\mathbb{R}^n \to \mathbb{R} +\] +If $f$ is smooth, $\frac{\partial f}{\partial x}(x^*) = 0$ at a local minimum.\\ Hence, now we have a root-finding problem $\nabla f(x) = 0$ $\Rightarrow$ Apply Newton! -$$ +\medskip + +% --- second part appears on next advance, first part stays visible --- +\only<2->{ + +\[ \nabla f(x+\Delta x) \approx \nabla f(x) + \frac{\partial}{\partial x}(\nabla f(x))\Delta x = 0 -\quad \quad \quad \quad -\Rightarrow \Delta x = -(\nabla^2 f(x))^{-1}\nabla f(x) -$$ +\quad\Rightarrow\quad +\Delta x = -(\nabla^2 f(x))^{-1}\nabla f(x) +\] -$$ +\[ x \leftarrow x + \Delta x -$$ +\] Repeat this step until convergence; Intuition to have about Newton: \begin{itemize} \item Fitting a quadratic approximation to $f(x)$; Exactly minimize approximation -\end{itemize} - +\end{itemize} +} \end{frame} @@ -99,58 +161,91 @@ \section{Root-Finding} \begin{frame}{Take-away Messages on Newton} -Newton is a local root-finding method. Will converge to the closest fixed point to the initial guess (min, max, saddle). +Newton is a local root-finding method. Will converge to the closest fixed point +to the initial guess (min, max, saddle). +\bigskip \textbf{Sufficient Conditions} \begin{itemize} - \item $\nabla f = 0$: “first-order necessary condition” for a minimum. Not a sufficient condition. - \item Let’s look at scalar case: $\Delta x = -\frac{1}{\nabla^2 f}\nabla f$ -\end{itemize} -where: negative corresponds to “descent”, $\nabla f$ corresponds to the gradient and $\nabla^2 f$ acts as the “leading rate” / “step size”. + \item $\nabla f = 0$: “first-order necessary condition” for a minimum. + Not a sufficient condition. + \item Let’s look at scalar case: $\Delta x = -\frac{1}{\nabla^2 f}\nabla f$ +\end{itemize} + +\medskip +where: negative corresponds to “descent”, $\nabla f$ corresponds to the gradient +and $\nabla^2 f$ acts as the “leading rate” / “step size”. +\end{frame} + + +\begin{frame}{Take-away Messages on Newton (cont’d)} +\[ +\nabla^2 f > 0 \quad \Rightarrow \quad \text{descent (minimization)} +\qquad +\nabla^2 f < 0 \quad \Rightarrow \quad \text{ascent (maximization)} +\] -$\nabla^2 f > 0 \quad \Rightarrow \quad \text{descent (minimization)} \quad \quad \quad \nabla^2 f < 0 \quad \Rightarrow \quad \text{ascent (maximization)}$ \begin{itemize} \item In $\mathbb{R}^n$, if $\nabla^2 f \succeq 0$ (positive definite) $\Rightarrow$ descent \item If $\nabla^2 f > 0$ everywhere $\Rightarrow f(x)$ is strongly convex → Can always solve with Newton \item Usually not the case for hard/nonlinear problems \end{itemize} - \end{frame} +\end{frame} \begin{frame}{Regularization: Ensuring Local Minimization} -Practical solution to make sure we always minimize: - + +\uncover<1->{\textbf{Practical solution to make sure we always minimize:}} + +\vspace{0.6em} + +\uncover<2->{ If $H$ ($H \leftarrow \nabla^2 f$) not positive definite, we just make it so with regularization. +\medskip While $H \not\succeq 0$: -$$H \leftarrow H + \beta I \quad (\beta > 0 \ \text{scalar hyperparameter})$$ - -Then do newton step as usual. I.e: +\[ +H \leftarrow H + \beta I \quad (\beta > 0 \ \text{scalar hyperparameter}) +\] +} -$$ -x \quad \leftarrow \quad x + \Delta x \quad = \quad x -H^{-1}\nabla f -$$ +\uncover<3->{ +Then do newton step as usual. I.e: +\[ +x \leftarrow x + \Delta x = x - H^{-1}\nabla f +\] \begin{itemize} \item also called “damped Newton” (shrinks steps) \item Guarantees descent \item Regularization makes sure we minimize, but what about over-shooting? -\end{itemize} +\end{itemize} +} + \end{frame} + \begin{frame}{Line Search: Mitigating overshooting in Newton} \begin{itemize} - \item Often $\Delta x$ step from Newton overshoots the minimum. - \item To fix this, check $f(x + \alpha \Delta x)$ and “back track” until we get a “good” reduction. - \item Many strategies: all differ in definition of good. - \item A simple + effective one is \textbf{Armijo Rule}: -\end{itemize} + \item<1-> Often $\Delta x$ step from Newton overshoots the minimum. + \item<1-> To fix this, check $f(x + \alpha \Delta x)$ and “back track” until we get a “good” reduction. + \item<1-> Many strategies: all differ in definition of good. + \item<2-> A simple + effective one is \textbf{Armijo Rule}: +\end{itemize} +\uncover<2->{ Start with $\alpha=1$ as our step length and have tolerance $b$ as a hyper-parameter. - $$ -\text{while } f(x + \alpha \Delta x) > f(x) + b \alpha \nabla f(x)^T \Delta x: \quad \quad \alpha \leftarrow c \alpha \quad (\text{scalar } < 1 \text{ i.e } c =\frac{1}{2}) -$$ -\footnotesize -The intuition behind this is that $\alpha \nabla f(x)^T \Delta x$ corresponds to the expected change in $f$ based on a 1st order taylor series expansion. I.e we are checking the actual decrease in $f$ agrees with a $1st$ order taylor approximation within a tolerance $b$. - -\end{frame} \ No newline at end of file +\[ +\text{while } f(x + \alpha \Delta x) > f(x) + b\,\alpha\, \nabla f(x)^{\!T} \Delta x +\quad\Longrightarrow\quad +\alpha \leftarrow c\,\alpha +\quad (\text{scalar } 0{ +{\footnotesize +The intuition: $\alpha\, \nabla f(x)^{\!T} \Delta x$ is the predicted change in $f$ from a first-order Taylor expansion. Armijo checks that the \emph{actual} decrease in $f$ matches this first-order prediction within tolerance $b$. +} +} +\end{frame} From b885e7aa401034fc0c27cfe28e944ba66d1d0a75 Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Thu, 4 Sep 2025 12:17:07 -0400 Subject: [PATCH 4/8] Add Class 2 HTML materials and documentation integration - Convert Jupyter notebooks to HTML with pre-run cells - Create comprehensive class02/overview.md with learning objectives - Update class02/class02.md with detailed content and links - Integrate Class 2 into documentation structure (docs/make.jl) - Add supporting materials: images, demo script, Project.toml - All materials now accessible through course documentation website --- class02/Manifest.toml | 7 + class02/Project.toml | 1 + class02/class02.md | 54 +- class02/log_barrier.png | Bin 0 -> 32399 bytes class02/overview.md | 115 + class02/part1_minimization.html | 15620 ++++++++++++++++++++++++++++ class02/part1_root_finding.html | 15263 +++++++++++++++++++++++++++ class02/part2_eq_constraints.html | 15414 +++++++++++++++++++++++++++ class02/part3_ipm.html | 15615 +++++++++++++++++++++++++++ class02/penalty_barrier_demo.py | 38 + class02/quadratic_penalty.png | Bin 0 -> 61491 bytes docs/make.jl | 11 +- 12 files changed, 62136 insertions(+), 2 deletions(-) create mode 100644 class02/Manifest.toml create mode 100644 class02/Project.toml create mode 100644 class02/log_barrier.png create mode 100644 class02/overview.md create mode 100644 class02/part1_minimization.html create mode 100644 class02/part1_root_finding.html create mode 100644 class02/part2_eq_constraints.html create mode 100644 class02/part3_ipm.html create mode 100644 class02/penalty_barrier_demo.py create mode 100644 class02/quadratic_penalty.png diff --git a/class02/Manifest.toml b/class02/Manifest.toml new file mode 100644 index 0000000..659f851 --- /dev/null +++ b/class02/Manifest.toml @@ -0,0 +1,7 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.11.6" +manifest_format = "2.0" +project_hash = "da39a3ee5e6b4b0d3255bfef95601890afd80709" + +[deps] diff --git a/class02/Project.toml b/class02/Project.toml new file mode 100644 index 0000000..81648c0 --- /dev/null +++ b/class02/Project.toml @@ -0,0 +1 @@ +[deps] diff --git a/class02/class02.md b/class02/class02.md index 5a23d52..f905c10 100644 --- a/class02/class02.md +++ b/class02/class02.md @@ -6,5 +6,57 @@ --- -Add notes, links, and resources below. +## Overview + +This class covers the fundamental numerical optimization techniques essential for optimal control problems. We explore gradient-based methods, Sequential Quadratic Programming (SQP), and various approaches to handling constraints including Augmented Lagrangian Methods (ALM), interior-point methods, and penalty methods. + +## Interactive Materials + +The class is structured around four interactive Jupyter notebooks: + +1. **[Part 1: Minimization via Newton's Method](part1_minimization.html)** + - Unconstrained optimization fundamentals + - Newton's method implementation + - Hessian matrix and regularization + +2. **[Part 1: Root Finding & Backward Euler](part1_root_finding.html)** + - Root-finding algorithms for implicit integration + - Fixed-point iteration vs. Newton's method + - Application to pendulum dynamics + +3. **[Part 2: Equality Constraints](part2_eq_constraints.html)** + - Lagrange multiplier theory + - KKT conditions for equality constraints + - Quadratic programming implementation + +4. **[Part 3: Interior-Point Methods](part3_ipm.html)** + - Inequality constraint handling + - Barrier methods and log-barrier functions + - Comparison with penalty methods + +## Additional Resources + +- **[Lecture Slides (PDF)](ISYE_8803___Lecture_2___Slides.pdf)** - Complete slide deck +- **[Demo Script](penalty_barrier_demo.py)** - Python demonstration of penalty vs. barrier methods +- **[LaTeX Source](main.tex)** - Source code for lecture slides + +## Key Learning Outcomes + +- Understand gradient-based optimization methods +- Implement Newton's method for minimization +- Apply root-finding techniques for implicit integration +- Solve equality-constrained optimization problems +- Compare different constraint handling methods +- Implement Sequential Quadratic Programming (SQP) + +## Prerequisites + +- Solid understanding of linear algebra and calculus +- Familiarity with Julia programming +- Basic knowledge of differential equations +- Understanding of optimization concepts from Class 1 + +## Next Steps + +This class provides the foundation for advanced topics in subsequent 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+ + + + + + + + + + + + + + + + diff --git a/class02/part1_root_finding.html b/class02/part1_root_finding.html new file mode 100644 index 0000000..214eeb8 --- /dev/null +++ b/class02/part1_root_finding.html @@ -0,0 +1,15263 @@ + + + + + +part1_root_finding + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/class02/part2_eq_constraints.html b/class02/part2_eq_constraints.html new file mode 100644 index 0000000..a9523a7 --- /dev/null +++ b/class02/part2_eq_constraints.html @@ -0,0 +1,15414 @@ + + + + + +part2_eq_constraints + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/class02/part3_ipm.html b/class02/part3_ipm.html new file mode 100644 index 0000000..8032014 --- /dev/null +++ b/class02/part3_ipm.html @@ -0,0 +1,15615 @@ + + + + + +part3_ipm + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/class02/penalty_barrier_demo.py b/class02/penalty_barrier_demo.py new file mode 100644 index 0000000..2893eaa --- /dev/null +++ b/class02/penalty_barrier_demo.py @@ -0,0 +1,38 @@ + +import numpy as np +import matplotlib.pyplot as plt + +def plot_log_barrier(save_path="log_barrier.png"): + x = np.linspace(1e-4, 1.0, 2000) + y = -np.log(x) + plt.figure() + plt.plot(x, y, linewidth=2) + plt.xlabel("x") + plt.ylabel("-log(x)") + plt.title("Log barrier: -log(x) vs x (blows up as x → 0⁺)") + plt.axvline(0.0, linestyle="--") + plt.ylim(0, min(15, float(np.max(y)))) + plt.grid(True, which="both", linestyle=":") + plt.tight_layout() + plt.savefig(save_path) + print(f"Saved {save_path}") + +def plot_quadratic_penalty(rhos=(1,10,100,1000,2500,5000), save_path="quadratic_penalty.png"): + x = np.linspace(-1.0, 1.0, 2000) + plt.figure() + for rho in rhos: + penalty = 0.5 * rho * np.minimum(0.0, x) ** 2 + plt.plot(x, penalty, linewidth=2, label=f"rho = {rho}") + plt.xlabel("x (feasible region is x ≥ 0)") + plt.ylabel("penalty(x) = (ρ/2)·min(0,x)²") + plt.title("Quadratic penalty for inequality constraint vs. ρ") + plt.axvline(0.0, linestyle="--") + plt.grid(True, which="both", linestyle=":") + plt.legend() + plt.tight_layout() + plt.savefig(save_path) + print(f"Saved {save_path}") + +if __name__ == "__main__": + plot_log_barrier() + plot_quadratic_penalty() \ No newline at end of file diff --git a/class02/quadratic_penalty.png b/class02/quadratic_penalty.png new file mode 100644 index 0000000000000000000000000000000000000000..53c4cb3fdf69356f1f1b6a3f47c8510520e7d4b1 GIT binary patch literal 61491 zcmc$`bySz_)-8M^h)5%d2uKKmB1%Xr-AD-tNVgy&CEZe@lp@k4B_gGSASn&fDbg(< z-Feon&-1?fobitFedBz8e2(qjZvFAQ@iy#Prtc-*Tf}HY3 z5R7pgZ1@}QuHk9;AO5G3nom`&&7L|L+LhEHuCTR(klVMOO>YG-d@{p8k7-kaR4 zbmmW=+Sm)Qv044s2X0#1J!D%;Ond-ea@I!Xfjxo{8KS>2-V0}1AjnFxtc0kVbNo_* zlO|c?N#mHC6Lp0gsRY(XO%f^=bu#VVItc~&r7LeGj9+jZ8yUHhg)oi1x9E@7JQosj z756f>8d-rd7x@yMs4IVN+X|5#mEw!)B0)2~4*M|sul8S)20TLTpO`&-%iu@MPJxf@ zTVuffUesg(`RC6R4gTE7#lL@l)%X9`KO#4@3afjwR6`sqF)*(>@*MjWTF+g2zR;c_v!$vF 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"class01_intro.html"), + joinpath(repo_dir, "class02", "part1_minimization.html"), + joinpath(repo_dir, "class02", "part1_root_finding.html"), + joinpath(repo_dir, "class02", "part2_eq_constraints.html"), + joinpath(repo_dir, "class02", "part3_ipm.html"), ] if !isdir(build_dir) symlink(joinpath(repo_dir, "class01"), joinpath(repo_dir, "docs", "src", "class01") ) + symlink(joinpath(repo_dir, "class02"), + joinpath(repo_dir, "docs", "src", "class02") + ) end makedocs( @@ -25,7 +32,7 @@ makedocs( assets = ["assets/wider.css", "assets/redlinks.css"], mathengine = Documenter.MathJax3(Dict( :tex => Dict( - "macros" => make_macros_dict("docs/src/assets/definitions.tex"), + "macros" => make_macros_dict("src/assets/definitions.tex"), "inlineMath" => [["\$","\$"], ["\\(","\\)"]], "tags" => "ams", ), @@ -36,6 +43,7 @@ makedocs( "Class 1" => ["class01/class01.md", "class01/background_materials/git_adventure_guide.md", ], + "Class 2" => "class02/overview.md", ], ) @@ -46,6 +54,7 @@ for pluto in plutos end rm(joinpath(repo_dir, "docs", "src", "class01"), force=true) +rm(joinpath(repo_dir, "docs", "src", "class02"), force=true) # In case we want to generate HTML from Pluto notebooks in CI # plutos = [ From 5644d4b184362ddcc895f890ed073a6c818604ba Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Thu, 4 Sep 2025 12:23:52 -0400 Subject: [PATCH 5/8] Fix make.jl paths and symlink creation - Fix definitions.tex path to be relative to docs/ directory - Always create symlinks instead of conditional creation - Ensure class01 and class02 directories are properly linked --- docs/make.jl | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 16d7a85..6b6fe3c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,14 +17,15 @@ plutos = [ joinpath(repo_dir, "class02", "part3_ipm.html"), ] -if !isdir(build_dir) - symlink(joinpath(repo_dir, "class01"), - joinpath(repo_dir, "docs", "src", "class01") - ) - symlink(joinpath(repo_dir, "class02"), - joinpath(repo_dir, "docs", "src", "class02") - ) -end +# Create symlinks to class directories +rm(joinpath(repo_dir, "docs", "src", "class01"), force=true) +rm(joinpath(repo_dir, "docs", "src", "class02"), force=true) +symlink(joinpath(repo_dir, "class01"), + joinpath(repo_dir, "docs", "src", "class01") +) +symlink(joinpath(repo_dir, "class02"), + joinpath(repo_dir, "docs", "src", "class02") +) makedocs( sitename = "LearningToControlClass", From 5731df2c413250f6f081526d12e9984357e6c7f3 Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Thu, 4 Sep 2025 12:28:19 -0400 Subject: [PATCH 6/8] Fix make.jl --- docs/make.jl | 19 +++++++++---------- 1 file changed, 9 insertions(+), 10 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 6b6fe3c..5897356 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,15 +17,14 @@ plutos = [ joinpath(repo_dir, "class02", "part3_ipm.html"), ] -# Create symlinks to class directories -rm(joinpath(repo_dir, "docs", "src", "class01"), force=true) -rm(joinpath(repo_dir, "docs", "src", "class02"), force=true) -symlink(joinpath(repo_dir, "class01"), - joinpath(repo_dir, "docs", "src", "class01") -) -symlink(joinpath(repo_dir, "class02"), - joinpath(repo_dir, "docs", "src", "class02") -) +if !isdir(build_dir) + symlink(joinpath(repo_dir, "class01"), + joinpath(repo_dir, "docs", "src", "class01") + ) + symlink(joinpath(repo_dir, "class02"), + joinpath(repo_dir, "docs", "src", "class02") + ) +end makedocs( sitename = "LearningToControlClass", @@ -33,7 +32,7 @@ makedocs( assets = ["assets/wider.css", "assets/redlinks.css"], mathengine = Documenter.MathJax3(Dict( :tex => Dict( - "macros" => make_macros_dict("src/assets/definitions.tex"), + "macros" => make_macros_dict("docs/src/assets/definitions.tex"), "inlineMath" => [["\$","\$"], ["\\(","\\)"]], "tags" => "ams", ), From 7295fa7901b6320b755c0bf6ea768ef691ab5177 Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Thu, 4 Sep 2025 12:45:03 -0400 Subject: [PATCH 7/8] clean up md files --- class02/class02.md | 23 ++++++++--------------- class02/overview.md | 21 +++++++++------------ 2 files changed, 17 insertions(+), 27 deletions(-) diff --git a/class02/class02.md b/class02/class02.md index f905c10..ea6746f 100644 --- a/class02/class02.md +++ b/class02/class02.md @@ -12,18 +12,19 @@ This class covers the fundamental numerical optimization techniques essential fo ## Interactive Materials -The class is structured around four interactive Jupyter notebooks: +The class is structured around 1 slide deck and four interactive Jupyter notebooks: -1. **[Part 1: Minimization via Newton's Method](part1_minimization.html)** - - Unconstrained optimization fundamentals - - Newton's method implementation - - Hessian matrix and regularization - -2. **[Part 1: Root Finding & Backward Euler](part1_root_finding.html)** +1. **[Part 1a: Root Finding & Backward Euler](part1_root_finding.html)** - Root-finding algorithms for implicit integration - Fixed-point iteration vs. Newton's method - Application to pendulum dynamics + +2. **[Part 1b: Minimization via Newton's Method](part1_minimization.html)** + - Unconstrained optimization fundamentals + - Newton's method implementation + - Globalization strategies: Hessian matrix and regularization + 3. **[Part 2: Equality Constraints](part2_eq_constraints.html)** - Lagrange multiplier theory - KKT conditions for equality constraints @@ -37,7 +38,6 @@ The class is structured around four interactive Jupyter notebooks: ## Additional Resources - **[Lecture Slides (PDF)](ISYE_8803___Lecture_2___Slides.pdf)** - Complete slide deck -- **[Demo Script](penalty_barrier_demo.py)** - Python demonstration of penalty vs. barrier methods - **[LaTeX Source](main.tex)** - Source code for lecture slides ## Key Learning Outcomes @@ -49,13 +49,6 @@ The class is structured around four interactive Jupyter notebooks: - Compare different constraint handling methods - Implement Sequential Quadratic Programming (SQP) -## Prerequisites - -- Solid understanding of linear algebra and calculus -- Familiarity with Julia programming -- Basic knowledge of differential equations -- Understanding of optimization concepts from Class 1 - ## Next Steps This class provides the foundation for advanced topics in subsequent classes, including Pontryagin's Maximum Principle, nonlinear trajectory optimization, and stochastic optimal control. diff --git a/class02/overview.md b/class02/overview.md index cff3ffd..6944190 100644 --- a/class02/overview.md +++ b/class02/overview.md @@ -34,20 +34,21 @@ By the end of this class, students will be able to: The class is structured around four interactive Jupyter notebooks that build upon each other: -1. **[Part 1: Minimization via Newton's Method](part1_minimization.html)** - - Unconstrained optimization fundamentals - - Newton's method for minimization - - Hessian matrix and positive definiteness - - Regularization and line search techniques - - Practical implementation with Julia -2. **[Part 1: Root Finding & Backward Euler](part1_root_finding.html)** +1. **[Part 1a: Root Finding & Backward Euler](part1_root_finding.html)** - Root-finding algorithms for implicit integration - Fixed-point iteration vs. Newton's method - Backward Euler implementation for ODEs - Convergence analysis and comparison - Application to pendulum dynamics +2. **[Part 1b: Minimization via Newton's Method](part1_minimization.html)** + - Unconstrained optimization fundamentals + - Newton's method for minimization + - Hessian matrix and positive definiteness + - Regularization and line search techniques + - Practical implementation with Julia + 3. **[Part 2: Equality Constraints](part2_eq_constraints.html)** - Lagrange multiplier theory - KKT conditions for equality constraints @@ -98,10 +99,6 @@ The methods covered in this class are fundamental to: ## Further Reading -- Nocedal, J., & Wright, S. J. (2006). *Numerical Optimization* -- Boyd, S., & Vandenberghe, L. (2004). *Convex Optimization* -- Betts, J. T. (2010). *Practical Methods for Optimal Control and Estimation Using Nonlinear Programming* - ## Next Steps This class provides the foundation for the advanced topics covered in subsequent classes, including: @@ -112,4 +109,4 @@ This class provides the foundation for the advanced topics covered in subsequent --- -*For questions or clarifications, please refer to the interactive notebooks or contact the instructor.* +*For questions or clarifications, please reach out to Arnaud Deza at adeza3@gatech.edu* From b37c41bf56c8bfeee685431cac0897bc99acdeeb Mon Sep 17 00:00:00 2001 From: ArnaudDeza Date: Thu, 4 Sep 2025 17:58:47 -0400 Subject: [PATCH 8/8] final html files and ipynb with explanations --- class02/part1_minimization.html | 54 +++++----- class02/part1_minimization.ipynb | 93 +++++++++-------- class02/part1_root_finding.html | 144 +++++++++++++++++++------- class02/part1_root_finding.ipynb | 119 ++++++++++++++++------ class02/part2_eq_constraints.html | 24 +++-- class02/part2_eq_constraints.ipynb | 156 ++++++++++++++++++++++++----- class02/part3_ipm.html | 20 +++- class02/part3_ipm.ipynb | 104 ++++++++++--------- 8 files changed, 490 insertions(+), 224 deletions(-) diff --git a/class02/part1_minimization.html b/class02/part1_minimization.html index b28bd94..593b414 100644 --- a/class02/part1_minimization.html +++ b/class02/part1_minimization.html @@ -14599,6 +14599,18 @@

+ + + + @@ -14972,7 +14984,7 @@

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2-element Vector{PyCall.PyObject}:
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1-element Vector{PyCall.PyObject}:
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Globalization Strategy 1: Regu @@ -15515,7 +15527,7 @@

Line-Search @@ -15582,30 +15594,14 @@

Line-Search - + PyObject <matplotlib.lines.Line2D object at 0x1705df850> + PyObject <matplotlib.lines.Line2D object at 0x1705df940> - diff --git a/class02/part1_minimization.ipynb b/class02/part1_minimization.ipynb index c1cf0aa..73053f6 100644 --- a/class02/part1_minimization.ipynb +++ b/class02/part1_minimization.ipynb @@ -8,6 +8,16 @@ "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()" ] }, + { + "cell_type": "markdown", + "id": "a155aec4", + "metadata": {}, + "source": [ + "# The content of this notebook comes from the CMU course \"Optimal-Control-16-745\" from Zachary Manchester:\n", + "\n", + "https://github.com/Optimal-Control-16-745/lecture-notebooks/blob/main/Lecture%203/minimization.ipynb" + ] + }, { "cell_type": "markdown", "id": "62dc7858", @@ -193,7 +203,7 @@ "data": { "text/plain": [ "1-element Vector{PyCall.PyObject}:\n", - " PyObject " + " PyObject " ] }, "execution_count": 6, @@ -242,7 +252,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 8, "id": "193f1b88", "metadata": {}, "outputs": [ @@ -260,10 +270,10 @@ "data": { "text/plain": [ "1-element Vector{PyCall.PyObject}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 21, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -276,13 +286,13 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "id": "ac35388f", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "Figure(PyObject
)" ] @@ -293,15 +303,12 @@ { "data": { "text/plain": [ - "5-element Vector{PyCall.PyObject}:\n", - " PyObject \n", - " PyObject \n", - " PyObject \n", - " PyObject \n", - " PyObject " + "2-element Vector{PyCall.PyObject}:\n", + " PyObject \n", + " PyObject " ] }, - "execution_count": 25, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -323,7 +330,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 10, "id": "5792cd59", "metadata": { "vscode": { @@ -345,10 +352,10 @@ "data": { "text/plain": [ "1-element Vector{PyCall.PyObject}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 26, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -361,7 +368,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 11, "id": "ce32e3d1", "metadata": { "vscode": { @@ -383,11 +390,11 @@ "data": { "text/plain": [ "2-element Vector{PyCall.PyObject}:\n", - " PyObject \n", - " PyObject " + " PyObject \n", + " PyObject " ] }, - "execution_count": 27, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -417,7 +424,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 12, "id": "82b98ed7", "metadata": { "vscode": { @@ -431,7 +438,7 @@ "-2.0" ] }, - "execution_count": 10, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -442,7 +449,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 13, "id": "7e12451f", "metadata": { "vscode": { @@ -456,7 +463,7 @@ "regularized_newton_step (generic function with 1 method)" ] }, - "execution_count": 11, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -474,7 +481,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 14, "id": "02b2106a", "metadata": { "vscode": { @@ -496,10 +503,10 @@ "data": { "text/plain": [ "1-element Vector{PyCall.PyObject}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 12, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -512,7 +519,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 15, "id": "7dcde9d4", "metadata": { "vscode": { @@ -534,11 +541,11 @@ "data": { "text/plain": [ "2-element Vector{PyCall.PyObject}:\n", - " PyObject \n", - " PyObject " + " PyObject \n", + " PyObject " ] }, - "execution_count": 13, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -568,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 16, "id": "6ae74c4d", "metadata": { "vscode": { @@ -582,7 +589,7 @@ "backtracking_regularized_newton_step (generic function with 1 method)" ] }, - "execution_count": 28, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -609,7 +616,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 17, "id": "9367632d", "metadata": { "vscode": { @@ -631,10 +638,10 @@ "data": { "text/plain": [ "1-element Vector{PyCall.PyObject}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 29, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -693,27 +700,19 @@ "plot(x, f(x))\n", "plot(xguess, f(xguess), \"rx\")" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d5ee59ea", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Julia 1.11.6", + "display_name": "Julia-Class02 1.10.0", "language": "julia", - "name": "julia-1.11" + "name": "julia-class02-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", - "version": "1.11.6" + "version": "1.10.0" } }, "nbformat": 4, diff --git a/class02/part1_root_finding.html b/class02/part1_root_finding.html index 214eeb8..8ce0797 100644 --- a/class02/part1_root_finding.html +++ b/class02/part1_root_finding.html @@ -14595,7 +14595,7 @@

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