Convex Optimization

Introduction

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms.

Contents

Convex Sets
Convex Functions
Convex Optimization Problems
Lagrangian and Lagrange Dual
Descent Methods in Unconstrained Optimization
Descent Methods in Equality Constrained Minimization
Interior Point Methods in Inequality Constrained Minimization
Differentiable Optimization

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Deep Declarative Network

Acknowledgement

This part is mainly based on the ANU course COMP4680 in 2023, convened by Prof. Stephen Gould.