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FG Kombinatorische Optimierung und GraphenalgorithmenConvex Optimization and Applications (ADM III)

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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:

  1. to provide the students with the necessary background to recognize optimization problems that can be reformulated as convex ones;
  2. 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);
  3. 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;
  4. 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

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):

www.thinfi.com/0zqp

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!

Exam Schedule
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

Chapter
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

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