Interior Point Methods

Overview

Explore advanced concepts in optimization with this lecture on Interior Point Methods, featuring insights from Steve Wright, Aaron Sidford, and Aleksander Mądry. Delve into the standard methods, key ideas, and applications of Interior Point Methods, including their relevance to the Maximum Flow Problem. Examine the Path Following Method, its analysis, and Renegar's Algorithm. Investigate the challenges in optimization and learn about the Regularized John Ellipse Barrier. Gain a deeper understanding of path finding techniques in the context of continuous and discrete optimization.

Syllabus

Intro
The Picture
Standard Methods
Why Study Interior Point Methods (IPM)?
Two Key Ideas for Interior Point Methods
The Maximum Flow Problem
Recap: Path Following Methods
Path Following Analysis
Renegar's Algorithm
What's the Problem?
Regularized John Ellipse Barrier
Path Finding