ECE236C - Optimization Methods for Large-Scale Systems

Course information

The course continues ECE236B and covers several advanced and current topics in optimization, with an emphasis on large-scale algorithms for convex optimization. This includes first-order methods for large-scale optimization (gradient and subgradient method, conjugate gradient method, proximal gradient method, accelerated gradient methods), decomposition and splitting methods (dual decomposition, augmented Lagrangian method, alternating direction method of multipliers, monotone operators and operator splitting), and (possibly) interior-point algorithms for conic optimization.

Lecture slides (Spring 2022)

Introduction
1. Gradient method
2. Subgradients
3. Subgradient method
4. Proximal gradient method
5. Conjugate functions
6. The proximal mapping
7. Accelerated proximal gradient methods
8. Proximal point method
9. Dual decomposition
10. Dual proximal gradient method
11. Douglas-Rachford splitting and ADMM
12. Primal-dual proximal methods
13. Conjugate gradient method
14. Newton's method
15. Quasi-Newton methods
16. Gauss-Newton method
17. Generalized distances and mirror descent
18. Generalized proximal gradient method

Lectures from previous years

Conic optimization and interior-point methods

First-order methods

Localization and cutting-plane methods

Exercises

A collection of exercises from homework assignments and discussions.