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Preliminary dates for the oral exam are:  February 28 and March 30. Please let us know soon in case you are not available at any of these dates.

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 problems;
  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
MA 649
Lecture
Thursday
14:15 - 15:45
MA 550

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

Contact Information

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. We expect a global understanding of how the chapters of this course articulate together. You will not be asked to prove results from the course, but you will have to solve some new exercises and show your modelling skills.

References

There will be a handout, posted online as the corresponding chapters are completed.

 

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.
  • "Semidefinite Optimization", Lecture notes of M. Laurent & F. Vallentin at Utrecht.

Further references are indicated directly in the handout.

Handout

Chapter
1-Preliminaries
1_intro.pdf
2-Convex geometry
2_cvx_geom.pdf
3-Convex functions
3_cvx_fun.pdf
4-Convex optimization
4_cvx_optim.pdf
5-Ellipsoid method
5_ellipsoid.pdf
6-Conic Programming
6_conic_programming.pdf
7-Duality
7_duality.pdf

 

 

Slides

Slides
1-Intro
slides-1.pdf
2-Convex geometry
slides-2.pdf
3-Convex functions
slides-3.pdf
4-Convex Optimization
slides-4.pdf
5-Ellipsoid Methods
slides-5.pdf

Exercise Sheets

Exercise Sheets
Exercise Sheet
Due Date
Sheet 1
Oct. 24
Sheet 2
Nov. 7
Sheet 3
Nov. 21

Zusatzinformationen / Extras

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