Instructor | Kuan Yang |
---|---|

Lecture times | `Friday` `16:00 - 17:40` (Week 1 - 16) `Wednesday` `8:00 - 9:40` (Even weeks) |

Location | Upper Hall 201 (上院 201) |

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

- Review of analysis; optimality condition

- Convex sets and their properties; separating hyperplane theorem
- Convex functions and their properties

- Geometric method and simplex algorithm
- LP duality and its applications

Unconstrained problem

- Descent methods: gradient descent and Newton's method
- Smooth and strongly convex functions
- Exact line search and backtracking line search

Equality constrained problem

- Lagrange's multiplier method
- Newton's method and KKT system

Inequality constrained problem

- KKT condition and Lagrange dual
- Projected gradient descent

Week | Date | Topics | Lecture notes | Homework |
---|---|---|---|---|

1 | 09/15 (Fri.) | Introductory examples | Lecture 01 / pdf | |

2 | 09/20 (Wed.) | Optimality condition, review of analysis | Lecture 02 / pdf | |

09/22 (Fri.) | Affinity (linearity) and convexity | Lecture 03 / pdf | HW1 | |

4 | 10/08 (Fri.) | Separating hyperplane theorem, supporting hyperplane theorem | ||

5 | 10/13 (Fri.) | Convex functions | ||

6 | 10/18 (Wed.) | Convex functions (cont'd) | ||

10/20 (Fri.) | Linear programming | |||

7 | 10/27 (Fri.) | LP duality and applications | ||

8 | 11/01 (Wed.) | Unconstrained optimization, gradient descent method | ||

11/03 (Fri.) | Analysis of gradient descent, smoothness and strong convexity | |||

9 | 11/10 (Fri.) | Condition number, line search | ||

10 | 11/15 (Wed.) | Newton's method | ||

11/17 (Fri.) | Proximal gradient descent | |||

11 | 11/24 (Fri.) | Lagrange multiplier method | ||

12 | 11/29 (Wed.) | Lagrange multiplier method (cont'd) | ||

12/01 (Fri.) | Newton's method and KKT system | |||

13 | 12/08 (Fri.) | KKT condition | ||

14 | 12/13 (Wed.) | Lagrangian and dual function | ||

12/15 (Fri.) | Dual problem and duality | |||

15 | 12/22 (Fri.) | Strong duality and Slater's condition | ||

16 | 12/27 (Wed.) | Projected gradient descent | ||

12/29 (Fri.) | Review and summary | Course summary |