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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 problem;
- 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.
Schedule
Day | Time | Room | |
---|---|---|---|
Lecture | Monday | 10:15 - 11:45 | Hauptgebäude H 1029 |
Lecture | Thursday | 14:15 - 15:45 | Hauptgebäude H 3006 |
An exercise session will be held every second week on Thursday.
Exceptionally, the lecture and exercises will be swapped in the first week of February:
* Exercises on Monday, February 5;
* Lecture on Thursday, February 8.
Contact Information
Lecturer: Dr. Guillaume Sagnol
Assistant: Daniel Schmidt gen. Waldschmidt
If you participate to this course, please enter your contact information here (The password will be given in class):
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.
The oral examinations will take place on February 26 - February 27.
Please register for one exam slot at Daniel Schmidt's office (MA 524) during office hours, starting from January 22, 2PM. You also need to register for the exam at the Prüfungsamt, and bring us the yellow registration form no later than February 15 (last lecture).
All exams will take place in MA 518. Don't forget to bring your student ID!
26. Feb | 27. Feb | ||
---|---|---|---|
Jeanny L. | 9:10 | ||
Antonia C. | 9:50 | Alexandra M. | 9:50 |
Rok F. | 10:30 | Robert S. | 10:30 |
Tomohiro K. | 11:10 | Norman H. | 11:10 |
Fabian W. | 11:50 | Ansgar R. | 11:50 |
Richard L. | 13:40 | Maximilian S. | 13:40 |
Ibrahim S. | 14:20 | Flora E. | 14:20 |
Forteinos M. | 15:00 |
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.
- "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
I - Preliminaries | chapter1_intro.pdf |
---|---|
II - Convex geometry | chapter2_convex_geometry.pdf |
III - Convex functions | chapter3_convex_functions.pdf |
IV - Convex optimization | chapter4_convex_optimization.pdf |
V- Conic programming | chapter5_conic_programming.pdf |
VI - Application to Data Analysis | chapter6_data_analysis.pdf |
VII - Duality | chapter7_duality.pdf |
VIII - SDP & Combinatorial Optimization | chapter8_combi.pdf |
IX - Robust Optimization | chapter9_robust_optim.pdf |
X - Interior Point Methods | chapter10_ipm.pdf |
XI - Polynomial Optimization | chapter11_poly_opt.pdf |