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

Lecture times | `Monday` `18:00 - 19:40` (Week 1 - 16) `Thursday` `08:00 - 09:40` (Even weeks) |

Location | Middle Hall 411 (中院 411) |

Teaching assistant(s) | Guoliang Qiu (邱国良) |

Office hours | `Wednesday` `14:00 - 15:00` at Room 1402, School of Software |

`12/28`

Homework 9 announced, due: Jan. 04.`12/17`

Homework 8 announced, due: Dec. 28.`12/07`

Homework 7 announced, due: Dec. 17.`11/19`

Homework 6 announced, due: Nov. 30.`11/02`

Homework 5 announced, due: Nov. 09.`10/22`

Homework 4 announced, due: Nov. 02.`10/15`

Homework 3 announced, due: Oct. 22.`10/08`

Homework 2 announced, due: Oct. 15.`09/22`

Homework 1 announced, due: Sept. 30.

*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

Week | Date | Topics | Materials | Homework |
---|---|---|---|---|

1 | 09/13 (Mon.) | Introduction to the course | Lec.1 manuscript | |

09/18 (W2 Mon.) | Analysis in vector spaces (I): compact sets, continuity, differential | Lec.2 manuscript | HW1 | |

2 | 09/23 (Thurs.) | Analysis in vector spaces (II): Hessian, definite matrices | Lec.3 manuscript | |

3 | 09/27 (Mon.) | Geometry: affine and convex sets, convex hull, polytope, simplex | Lec.4 manuscript | HW2 |

4 | 10/09 (W4 Thurs.) | Separating hyperplane theorem, supporting hyperplane theorem | Lec.5 manuscript | |

5 | 10/11 (Mon.) | Convex functions, midpoint convexity | Lec.6 manuscript | HW3 |

6 | 10/18 (Mon.) | First and second order conditions, convexity-preserving operations | Lec.7 manuscript | |

10/21 (Thurs.) | Convexity-preserving operations, inequalities, optimization problems | Lec.8 manuscript | HW4 | |

7 | 10/25 (Mon.) | Linear programming, simplex method | Lec.9 manuscript | |

8 | 11/01 (Mon.) | Farkas' lemma, duality of LP | Lec.10 manuscript | HW5 |

11/04 (Thurs.) | Applications of LP duality, unconstrained optimization, introduction to gradient descent | Lec.11 manuscript | ||

9 | 11/08 (Mon.) | Convergence of gradient descent, discrete-time Lyapunov's stability theorem, -smooth functions, convergence rate for fixed step size | Lec.12 manuscript | |

10 | 11/15 (Mon.) | -strongly convex functions, exponential convergence rate, exact line search method, Newton's method for finding roots | Lec.13 manuscript | |

11/18 (Thurs.) | Backtracking line search method, Newton's method for optimization | Lec.14 manuscript | HW6 | |

11 | 11/22 (Mon.) | Newton's method (cont'd), Proximal gradient descent | Lec.15 manuscript | |

12 | 11/29 (Mon.) | Properties of proximal mapping, equality constrained optimization, optimality condition for linear constraints, submanifolds | Lec.16 manuscript | |

12/02 (Thurs.) | Implicit function theorem, tangent space, differential on submanifolds, Lagrange multiplier | Lec.17 manuscript | ||

13 | 12/06 (Mon.) | Lagrange multiplier (cont'd), Second-order condition, Solving quadratic optimization | Lec.18 manuscript | HW7 |

14 | 12/13 (Mon.) | Newton's method, KKT condition | Lec.19 manuscript | |

12/16 (Thurs.) | KKT condition (cont'd), Lagrange dual | Lec.20 manuscript | HW8 | |

15 | 12/20 (Mon.) | Weak and strong duality, Slater's condition for convex problems | Lec.21 manuscript | |

16 | 12/27 (Mon.) | Projected gradient descent, introduction to interior-point methods | Lec.22 manuscript | HW9 |

12/30 (Thurs.) | Review and summary | Course summary |