# ECE236C - Optimization Methods for Large-Scale Systems

In Spring 2020, this course will be taught by
Jerome Bolte, Visiting Professor
at UCLA.

## Lecture notes (Spring 2019)

Introduction

Gradient method

Subgradients

Subgradient method

Proximal gradient method

Conjugate functions

The proximal mapping

Accelerated proximal gradient methods

Proximal point method

Dual decomposition

Dual proximal gradient method

Douglas-Rachford splitting and ADMM

Primal-dual proximal methods

Generalized distances and mirror descent

Generalized proximal gradient method

Conjugate gradient method

Newton's method

Quasi-Newton methods

Gauss-Newton method

## Lectures from previous years

Conic optimization and interior-point methods

First-order methods

Localization and cutting-plane methods

## Homework and project

Homework solutions are posted on the
CCLE course website.

## Course information

**Description.**
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 notes.**
The lecture notes will be posted on this website. Many of the topics
are covered in the following books and in the
course EE364b (Convex Optimization II) at Stanford University.

A. Beck,
*First-Order Methods in Optimization*, SIAM.

D. Bertsekas,
*Convex Optimization Algorithms*, Athena Scientific.

D. Bertsekas and J. Tsitsiklis,
*Parallel and Distributed Computation*,
Athena Scientific.

Yu. Nesterov,
*Lectures on Convex Optimization*, Springer.

J. Nocedal and S. Wright,
*Numerical Optimization*, Springer.

B. T. Polyak, *Introduction to Optimization*, Optimization Software.

**Course requirements**. Weekly homework assignments and a project.

**Grading**.
Approximate weights in the final grade: homework 30%, project 70%.