### Inhalt des Dokuments

## News

**Change of schedule**

Exceptionally, there will be an exercise session on Monday, February 4 (10:15).

A regular class will take place on Thursday, January 31 (14:15).

**Registration to the exam**

Some student had troubles with the administration to register to the exam. The issue has been settled, and the lecture now appears in the list of valid modules at the Prüfungsamt, so you can enroll to the exam now. Please remember to bring your yellow registration form by February 14th.

# Convex Optimization and Applications (ADM III)

Surprisingly many real-world optimization problems can be reformulated as convex optimization problems. This convexity plays a central role in the computational tractability of a solution. The goals of this course are:

- to provide the students with the necessary background to recognize optimization problems that can be reformulated as convex ones;
- to study the duality theory of convex optimization from the point of view of conic programming, which includes as particular cases the linear programming (LP), semidefinite programming (SDP), second order cone programming (SOCP), and geometric programming (GP);
- to review a variety of applications of convex optimization from various branches such as engineering, control theory, machine learning, robust optimization, and approximation algorithms for combinatorial problems;
- finally, to understand algorithms for convex programming, in particular interior point methods, and to be able to use modern interfaces to pass optimization problems to solvers that implement these algorithms.

# Examination

The oral examinations will take place **on February 28 and March 29**.

Please register for one exam slot at Daniel Schmidt's office (MA 524) during office hours, starting from January 21, 2PM. You also need to register for the exam at the Prüfungsamt, and bring us the yellow registration form **no later than February 14** (last lecture).

All exams will take place in MA 518. Don't forget to bring your student ID!

For the examinations, you are not expected to know everything *by heart. *However, you have to know the basic definitions, know which results exist, and be able to explain them with your own words (there is no need to know very technical formulas, but you must be able to restitute the main message of a theorem, for example. If you ever need a technical formula, there will be a printed copy of the handout available during the exam. You will not be asked to prove results from the course, but rather to demonstrate your general understanding on convex optimization techniques, solve some new exercises, and show your modelling skills.

28. Feb | 29. Mar | ||
---|---|---|---|

Lukas S. | 8:30 | ||

Sebastian O. | 9:10 | ||

Daniel O. | 9:50 | Alicia B. | 9:50 |

Hazem L. | 10:30 | Minh P. | 10:30 |

Elaine Z. | 11:10 | Zhengge Z. | 11:10 |

Gioni M. | 11:50 | ||

Nikolai H. | 13:40 | ||

Tim G. | 14:20 | Jonas K. | 14:20 |

Thomas N. | 15:00 | Michael D. | 15:00 |

Rick G. | 15:40 | ||

Eli V. | 16:20 | ||

Marcel M. | 17:00 |

## Schedule

Day | Time | Room | |
---|---|---|---|

Lecture | Monday | 10:15 - 11:45 | MA 841 |

Lecture | Thursday | 14:15 - 15:45 | MA 841 |

An exercise session will be held every second week on Thursday.

## Evaluation

**Exercises** will be given on week in advance. At the beginning of exercise sessions, check the exercises you've prepared. One student will be asked to explain his solution. You need 50% of all exercises *checked* to take the exam.

There will be an **oral examination**. You should not learn everything *by heart*, but rather know which result exists and be able to find it in your handout if needed. You will not be asked to prove results from the course, but rather to demonstrate your general understanding on convex optimization techniques, solve some new exercises, and show your modelling skills.

## References

There will be a handout, put online as and when the corresponding chapters are finished.

The course is mainly based on:

- Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.

Selected chapters are also based on the following references:

- "Lecture on Modern Convex Optimization", A. Ben-Tal & A. Nemirovski, 2001.
- "Linear and Semidefinite Programming", Lecture notes of A. Gupta and R. O'Donell at Carnegie Mellon.
- "Topics in Convex Optimisation", Lecture notes of H. Fawzi at Cambridge.
- "Approximation Algorithms and Semidefinite Programming", Lecture notes of B. Gärtner & J. Matoušek at ETH Zurich.
- "Semidefinite Optimization", Lecture notes of M. Laurent & F. Vallentin at Utrecht.

Further references are indicated directly in the handout.

## Handout

1 - Preliminaries | chapter1_intro.pdf |
---|---|

2 - Convex geometry | chapter2_convex_geom.pdf |

3 - Convex functions | chapter3_convex_fun.pdf |

4 - Convex optimization problems | chapter4_convex_optim.pdf |

5 - Ellipsoid methods | chapter5_ellipsoid.pdf |

6 - Conic programming | chapter6_conic_prog.pdf |

7 - Duality | chapter7_duality.pdf |

8 - Application to combinatorial optimization problems | chapter8_combi.pdf |

9 - Interior point methods | chapter9_ipm.pdf |

10 - Application to data analysis | chapter10_data.pdf |

11 - First order methods for large scale problems | chapter11_fom.pdf |

## Slides

1-Intro | slides-1.pdf |
---|---|

2-Convex geometry | slides-2.pdf |

3-Convex functions | slides-3.pdf |

4-Convex optimization problems | slides-4.pdf |

5-Ellipsoid methods | slides-5.pdf |

9-Interior point methods | slides-9.pdf |

10-Data Analysis | slides-10.pdf |

11-First order methods | slides-11.pdf |

12-Advanced topics | slides-12.pdf |