Convex Optimization Projects (MGT-418)

This repository contains two applied convex optimization assignments completed for
MGT-418: Convex Optimization (EPFL).

Each assignment is organized in its own directory and includes the problem statement, implementation, and written report.

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1. Smooth Hinge Loss Support Vector Machines

Description:
Support Vector Machines trained with a smooth hinge loss, emphasizing convex reformulations, duality, and kernel methods.

Directory: Smooth-Hinge-Loss-SVMs/

Files:

• p2q2.py – Linear SVM via QCQP (CVXPY)
• p2q3.py – Kernel SVM (dual formulation, Gaussian kernel)
• report.pdf – Theory, derivations, and results
• HingeLoss_Questions.pdf – Assignment problem statement

Topics:

• Smooth hinge loss via infimal convolution
• QCQP reformulation
• Duality and KKT conditions
• Kernel SVMs

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2. D-Optimal and G-Optimal Experimental Design

Description:
Convex optimization methods for optimal experimental design, focusing on the equivalence between D-optimal and G-optimal criteria.

Directory: D-and-G-Optimal-Experimental-Design/

Files:

• p5q31.py – D-optimal and G-optimal design (CVXPY, SDP)
• p5q32.py – Frank–Wolfe algorithm and visualization
• report.pdf – Theory, proofs, and experiments
• ExperimentalDesign_Questions.pdf – Assignment problem statement

Topics:

• D-optimal vs G-optimal design
• Semidefinite programming
• Frank–Wolfe (conditional gradient) methods
• Optimality conditions and geometry