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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:

  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.

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.

 

Exam Schedule
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

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.

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 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

Chapter
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

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

Exercise Sheets

Exercise Sheets
Exercise Sheet
Due Date
Sheet 1
Nov. 01
Sheet 2 
Nov. 15
Sheet 3
Nov. 29
Sheet 4
Dec. 13
Sheet 5
Jan. 17
Sheet 6
Feb. 4

Zusatzinformationen / Extras

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