| Instructor | Kuan Yang |
|---|---|
| Lecture times | Friday 16:00 - 17:40 (Odd weeks) Tuesday 8:00 - 9:40 (Week 1 - 16) |
| Location | Middle Hall 213 (中院 213) |
| Teaching assistant(s) | Yao Xu (徐遥) |
| Office hours | To be determined |
Convex Optimization by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press
An Introduction to Optimization by Edwin K. P. Chong and Stanislaw H. Żak, Wiley.
(中文翻译版：最优化导论（第四版），电子工业出版社)
Large-Scale Optimization for Data Science at Princeton
Convex Optimization at CMU
Unconstrained problem
Equality constrained problem
Inequality constrained problem
| Week | Date | Topics | Lecture notes | Homework |
|---|---|---|---|---|
| 1 | 09/20 (Fri.) | Introductory examples | Lecture 01 / pdf | |
| 2 | 09/24 (Tue.) | Optimality condition, review of analysis | Lecture 02 / pdf | |
| 4 | 10/08 (Tue.) | Affinity (linearity) and convexity | Lecture 03 / pdf | HW1 |
| 5 | 10/15 (Tue.) | Separating hyperplane theorem, supporting hyperplane theorem | Lecture 04 | |
| 10/18 (Fri.) | Convex functions | Lecture 05 | ||
| 6 | 10/22 (Tue.) | Convex functions (cont'd) | Lecture 06 | |
| 7 | 10/29 (Tue.) | Linear programming | Lecture 07 | |
| 11/01 (Fri.) | LP duality and applications | Lecture 08 | ||
| 8 | 11/05 (Tue.) | Unconstrained optimization, gradient descent method | Lecture 09 | |
| 9 | 11/12 (Tue.) | Analysis of gradient descent, smoothness and strong convexity | Lecture 10 | |
| 11/15 (Fri.) | Condition number, line search | Lecture 11 | ||
| 10 | 11/19 (Tue.) | Newton's method | Lecture 12 | |
| 11 | 11/26 (Tue.) | Proximal gradient descent | Lecture 13 | |
| 11/29 (Fri.) | Lagrange multiplier method | Lecture 14 | ||
| 12 | 12/03 (Tue.) | Lagrange multiplier method (cont'd) | ||
| 13 | 12/10 (Tue.) | Newton's method and KKT system | Lecture 15 | |
| 12/13 (Fri.) | KKT condition | Lecture 16 | ||
| 14 | 12/17 (Tue.) | Lagrangian and dual function | ||
| 15 | 12/24 (Tue.) | Dual problem and duality | Lecture 19 | |
| 12/27 (Fri.) | Strong duality and Slater's condition | |||
| 16 | 12/31 (Tue.) | Projected gradient descent, review and summary | Course summary | Lecture 17 Lecture 18 |