Aaron Sidford (sidford@stanford.edu)

Welcome

This page has informatoin and lecture notes from the course "Introduction to Optimization Theory" (MS&E213 / CS 269O) which I taught in Spring 2017. I hope you enjoy the content as much as I enjoyed teaching the class and if you have questions or feedback on the note, feel free to email me.

Course Overview

This class will introduce the theoretical foundations of continuous optimization. Starting from first principles we show how to design and analyze simple iterative methods for efficiently solving broad classes of optimization problems. The focus of the course will be on achieving provable convergence rates for solving large-scale problems.

Email: sidford@stanford.edu

Here are the links for the course lecture notes. Feedback is welcome and if there is anything that is unclear or you would like added, please feel free to contact me. My apologies for missing citations and references; these may be added over time in future course offerings

**Chapter 1: Introduction**: The notes for this chapter are here.**Chapter 2: Smoothness**: The notes for this chapter are here.**Chapter 3: Convexity**: The notes for this chapter are here.**Chapter 4: Acceleration**: The notes for this chapter are here.**Chapter 5: Smooth Extensions**: The notes for this chapter are here.**Chapter 6: Non-smooth Convex Functions**: The notes for this chapter are here.**Chapter 7: Cutting Plane Methods**: The notes for this chapter are here.**Chapter 8**:**Subgradient / Mirror Descent**: The notes for this chapter are here.**Chapter 9: Interior Point Methods**: The notes for this chapter are here.**Appendix A: Norms**: The notes for this chapter are here.

The material in the lecture notes is based primarily on my own experience with optimization and the following two texts:

- "Introductory Lectures on Convex Programming Volume I: Basic Course" by Yurii Nesterov.
- Convex Optimization: Algorithms and Complexity by Sébastien Bubeck.

Additional resources that may be helpful include the following:

- Convex Optimization by Stephen Boyd and Lieven Vandenberghe.
- CSE 599: Interplay between Convex Optimization and Geometry a course by Yin Tat Lee.