Tue/Thu, 3:00-4:30pm, Towne 321

Shuo Han

Office hour: Wed, 2:00-4:00pm, Moore 317

Andreea Alexandru

Office hour: Tue, 12:30-2:30pm, GRASP conference room (4th floor of Levine, next to the elevators)

Yicheng Lin (Grader)

This course concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: convex sets, functions, and optimization problems. Basis of convex analysis. Linear, quadratic, geometric, and semidefinite programming. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods, ellipsoid algorithm and barrier methods, self-concordance. Applications to signal processing, control, digital and analog circuit design, computation geometry, statistics, and mechanical engineering.

Working knowledge of linear algebra. Exposure to real analysis and probability. Familiarity with MATLAB. Undergraduates need permission from instructor.

Date | Topic | Reading | Homework |
---|---|---|---|

Week 1 1/12 |
Introduction | Chapter 1 Appendix A |
Sign up for Piazza |

Week 2 1/17, 1/19 |
Convex sets | Chapter 2 | Homework 1 (due: 1/26) |

Week 3 1/24, 1/26 |
Convex functions | Chapter 3 | Homework 2 (due: 2/2) |

Week 4 1/31, 2/2 |
Convex optimization problems | Chapter 4 | Homework 3 (due: 2/14) |

Week 5 2/7, 2/9 |
Convex optimization problems Duality |
Chapter 4, 5 | Homework 4 (TBD) |

Week 6 2/14, 2/16 |
Duality | Chapter 5 | Homework 5 (due: 2/23) |

Week 7 2/21, 2/23 |
Unconstrained minimization | Chapter 9 | Homework 6 (due: 3/2) |

Week 8 2/28, 3/2 |
Equality constrained minimization | Chapter 10 | Homework 7 (due: 3/16) |

Spring break | |||

Week 9 3/14, 3/16 |
Inequality constrained minimization Interior-point methods |
Chapter 11 | Homework 8 (due: 3/23) |

Week 10 3/21, 3/23 |
Application: Approximation and fitting | Chapter 6 | Homework 9 (due: 4/2) |

Week 11 3/28, 4/2 |
Application: Statistical estimation | Chapter 7 | Homework 10 (due: 4/6) |

Week 12 4/4, 4/6 |
Application: Geometric problems | Chapter 8 | Homework 11 (due: 4/13) |

Week 13 4/11, 4/13 |
Advanced topic: Convex relaxation | TBA | Homework 12 (due: 4/20) |

Week 14 4/18, 4/20 |
Advanced topic (time permitting) | TBA | No homework |

Week 15 4/25 |
Conclusions | N/A | Final exam |

- Homework (40%): Homework sets are issued every Thursday and are due the following Thursday in class.
- Final exam (60%): There will be an open-book, take-home final exam. The exam will be available online on 4/25 after class. You may need to use MATLAB for some of the problems.

**Late homework**: Late homework will not be accepted without a note from the Student Health Service or the (Associate) Dean.**Collaboration**- Collaboration on homework assignments is encouraged. You may consult the textbook, other references listed on the course webpage, other students, the TA, or the instructor. You may also consult outside references not listed on the course webpage, provided that you cite those references in your homework solutions.
- You cannot consult homework solutions from prior years or solution manuals. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing.
- MATLAB scripts and plots are considered part of your writeup and should be done individually (you can share ideas, but not code).
- No collaboration is allowed on the final exam.

The required text for the course is

- S. P. Boyd and L. Vandenberghe,
*Convex Optimization*, Cambridge University Press, 2004. Online access. Hard copies are available at the Penn Bookstore. - Some homework problems come from the additional exercises accompanied with the textbook.

The following additional references may also be useful:

- A. Ben-Tal and A. Nemirovski,
*Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications*, SIAM, 2001. Online access. - D. P. Bertsekas, A. Nedic, and A. E. Ozdaglar,
*Convex Analysis and Optimization*, Athena Scientific, 2003.