Current Problems in Applied Mathematics: Convex Optimization

The following is a **tentative** syllabus for the course.
Lecture notes will be available here.

Week # | Description and Lecture Note | Last Updated |
---|---|---|

1-2 | Part 1: Convex Sets, Functions and Optimization | Jan 17 (W) 3:40 PM |

3-4 | Part 2: Gradient and Subgradient Methods for Unconstrained Convex Optimization | Jan 29 (M) 3:23 PM |

5 | Part 3: Projected and Proximal Gradient Methods | Feb 5 (M) 3:24 PM |

6-7 | Part 4: KKT Conditions and Duality | Feb 16 (F) 3:26 PM |

8 | Part 5: Dual-based Methods | Feb 25 (Su) 1:18 PM |

9 | Part 6: Newton's Method | Feb 28 (W) 3:35 PM |

The following is a **tentative** daily schedule for the course.
This page will be updated irregularly.

Date | Description | |
---|---|---|

Part 1 | Jan 3 (W) | Introduction to Convex Optimization 1 |

Jan 5 (F) | Introduction to Convex Optimization 2, Mathematical Preliminaries | |

Jan 8 (M) | Convex Sets | |

Jan 10 (W) | Convex Functions | |

Jan 12 (F) | Convex Optimization 1 | |

Jan 17 (W) | Convex Optimization 2 | |

Part 2 | Jan 18 (Th) | Gradient Methods |

Jan 19 (F) | Convergence Rate of Gradient Methods 1 | |

Jan 22 (M) | Convergence Rate of Gradient Methods 2, Lower Complexity Bounds of Gradient Methods | |

Jan 24 (W) | Accelerated Gradient Methods | |

Jan 26 (F) | Subgradients | |

Jan 29 (M) | Subgradient Methods | |

Part 3 | Jan 31 (W) | Projected Subgradient Methods, Mirror Descent Methods |

Feb 2 (F) | Proximal Operator, Proximal Gradient Methods | |

Feb 5 (M) | Accelerated Proximal Gradient Methods, Proximal Point Methods | |

Part 4 | Feb 7 (W) | Optimality Conditions for Linearly Constrained Problems |

Feb 9 (F) | KKT Conditions 1 | |

Feb 12 (M) | KKT Conditions 2 | |

Feb 14 (W) | Lagrange Duality 1 | |

Feb 15 (Th) | Lagrange Duality 2 | |

Feb 16 (F) | Lagrange Duality 3 | |

Part 5 | Feb 19 (M) | Dual Projected Subgradient Methods, Dual Proximal Gradient Methods |

Feb 21 (W) | Augmented Lagrangian Methods (Method of Multipliers) | |

Feb 23 (F) | Alternating Direction Method of Multipliers (ADMM) | |

Part 6 | Feb 26 (M) | Newton's Method |

Feb 28 (W) | Newton's Method with Equality and Inequality Constraints | |

Project | Mar 2 (F) | Presentation |

Mar 5 (M) | Presentation |