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Fundamentals of Convex Optimization (MA2504)


lecturer: Prof. Dr. Peter Gritzmann
learning assistant and organization: Dr. René Brandenberg

News Dates of lectures/exercise classes and office hours Lecture notes Problem sheets Exam Literature FAQ


  • July 14th: If you want to hand in your solutions of Sheet 13, please do until friday this week. We'll try to do corrections until tuesday after and put them in the usual shelves.
  • July, 13th: The list of the homework points after corrections of Sheet 11 hangs in the showcase of M9 at the corner before going into the M9 finger 02.04.xxx.
  • July, 9th: Sheet 12 is the last that counts for the 80% mark to obtain the homework-bonus. We will hand out a Sheet 13 next week, but if there are homeworks still corrected than on a voluntary basis. We will hang out a list of the homework points made as soon as Shee11 is corrected.
  • June,15th: the lecture on friday, 18th must be canceled due to the faculty day.
  • May, 26th: Sheet 6 is now online!
  • May, 21st: due to the teaching free tuesday next week (may, 26th) and the postponed lectures of that week, also the exercise groups on wednesday (may, 27th) are canceled!
    Please submit your solution for exercise sheet 5 until tuesday, june, 2nd (usual time). We will upload a small sheet 6 the next days, which will ot count for the bonus system. Its solution will be given in the next exercise groups.
  • Mar, 27th: Welcome to the homepage of the course on convex optimization, summer term 2015.


The exam takes place on 24th of July, 11.00-12.30 in MW 0001. It is a closed book examination.
The 2nd exam takes place on 2nd of October, 11.00-12.30 in Interimshörsaal 1. It is a closed book examination again.

Because we were frequently asked we attached some exams of the previous years. Be aware that the courses may differ from year to year and therefore the things to be able to do in the exam may differ.

Dates of lectures/exercise classes and office hours

Type Day Time Room Teacher/Tutor Language Comment
Lecture 1 Monday 16:00 - 17:30 MI HS 1 Gritzmann english see TUMonline or the attached pdf for details of the schedule
Lecture 2 Thursday 14.15 - 15:45 MI HS 3 Gritzmann english see TUMonline or the attached pdf for details of the schedule
Lecture 3 Friday 14:00 - 15:30 MI HS 1 Gritzmann english see TUMonline or the attached pdf for details of the schedule
Exercise class 1 Tuesday 08:10 - 09:55 02:04:011 Brandenberg german
Exercise class 2 Tuesday 10:15 - 12:00 02:08:011 Gonzáles english
Exercise class 3 Tuesday 10:15 - 12:00 02:04:011 Brandenberg german
Exercise class 4 Wednesday 10:05 - 11:50 02:08:011 Brandenberg german
Exercise class 5 Wednesday 12:15 - 14:00 02:04:011 Gonzáles canceled from July, 1st
Exercise class 6 Wednesday 8:15 - 10:00 02:08:020 Niels german

Exercise class "Bonus without visiting classes" : is meant for those who know for sure that they will not attend the classes but want to participate in the homework bonus. Even so offering the "Bonus without visiting classes" opertunity, we strongly recomand to visit the exercise classes as the final exam will be based on both, lectures and exercise classes.

Office hours

Person Office hours (during semester)
Prof. Dr. Peter Gritzmann Friday, 16-17 h (on all Fridays when there are lectures) or by appointment
Dr. René Brandenberg on appointment
Bernardo Gonzáles Merino  

Lecture notes

Problem sheets

Problem sheets Solution outlines Supplementary sheets (voluntary) Comments
Sheet 01 Solution outlines 01    
Sheet 02 Solution outlines 02 Supplementary sheet 02  
Sheet 03 Solution outlines 03    
Sheet 04 Solution outlines 04 Supplementary sheet 04  
Sheet 05 Solution outlines 05   solution updated, small errors in 5.1e and 5.2a corrected
Sheet 06 Solution outlines 06 Supplementary sheet 06 no submission
Sheet 07 Solution outlines 07   hint added for exercise 7.1
Sheet 08 Solution outlines 08   added in 8.1 that F should be a proper face
Sheet 09 Solution outlines 09 Supplementary sheet 09  
Sheet 10 Solution outlines 10    
Sheet 11 Solution outlines 11    
Sheet 12 Solution outlines 12 Supplementary sheet 12  
Sheet 13 Solution outlines 13   submission until friday on voluntary base, we'll try to correct it until tuesday after

Please use the attached cover sheet when handing in your homework.

Grade boni for homework participation (Notenbonus)

For the continuous participation in the exercise classes you may achieve a grade bonus in your exam. Modalities are as following:
  • You have to be registered in TUMonline for one of the exercise classes! (See TUMonline for the deadline.) Otherwise your homework points will not be recorded.
  • If you get the mark "reasonably treated" in at least 80% of your homework, you obtain a bonus of one degree step for a passed exam, i.e. for example a 1.7 becomes a 1.3, a 2.3 becomes a 2.0, and a 3.0 becomes a 2.7.
  • A handed in solution of a homework problem gets the mark "reasonably treated", if the corrector may observe that you well treated the problem from a mathematical point of view. It is not necessary that this treatment leads to a correct solution!
  • Multiple-Choice-sheets are extra sheets and do not count for the homework bonus.
  • Exam grades, which do not suffice to pass the exam without bonus (4.3,4.7,5.0) cannot be improved from a homework bonus. The same is true for a grade of 1.0 in the exam.
  • Any obtained homework bonus is valid for both exams belonging to the course in the semester it is obtained in, but cannot be kept for the same course in later semesters.


  • A. Barvinok: A course in convexity, American Mathematical Society, Providence, RI, 2002
  • A. Ben-Tal, A. Nemirowski: Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization
  • D. P. Bertsekas, A. Nedic, A. E. Ozdaglar. Convex Analysis and Optimization, Athena Scientific, 2003
  • T. Bonnesen, W. Fenchel: Theorie der konvexen Körper (korr. Nachdruck), Springer, 1974
  • C. Geiger, C. Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002
  • P.E. Gill, W. Murray, M.H. Wright: Practical Optimization, Academic Press, 1981
  • P. Gritzmann: Grundlagen der mathematischen Optimierung, Springer, 2013
  • B. Grünbaum: Polytopes, Springer, 1993
  • F. Jarre, J. Stoer: Optimierung, Springer, 2004 * M. Minoux: Mathematical Programming: Theory and Algorithms, Wiley, 1986
  • R. T. Rockafellar. Convex Analysis. Princeton University Press, 1972
  • C.Roos, T. Terlaky, J.P. Vial: Theory and Algorithms for Linear Optimization: An Interior Point Approach, 1997
  • R. Schneider: Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, 1993
  • R. J. Vanderbei. Linear Programming, Foundations and Extensions. Springer, 2008


question How does the allocation of the exercise classes work?
info As following:
  • The exercises take place almost every week, the exact data can be found under Dates of lectures/exercise classes and office hours.
  • The registration into the exersise classes has to be done via TUMonline. Mind the deadlines given in TUMonline!
  • First, there will only be the exercise classes already listed under Dates of lectures/exercise classes and office hours. In each of the classes a given maximum number of people can be registered.
  • If the number of registrations into one of the groups reaches the limit, we will try to offer an additional class at the same appointed time. If so, we will inform you under News as soon as possible
  • As long as the registration is open and there are remaining places, you can subscribe and unsubscribe into the groups as you want.
  • Multiple subscriptions are not allowed!

question Will there be a written exam?
info Yes. Some information about the exams can be found under this link. We will inform you via this web-page as soon as the schedule of the exam is fixed.

question Do I have to register for the exam?
info Yes, you have to register via TUM-Online. A "how-to" can be downloaded here (pdf)

question Which additives are allowed to be used during the exam?
info None, except writing utensils.

question Am I automatically signed up for the repetition exam if I failed the first one?
info No. You have to sign up again.

question How does the Homework system work for the exercises?
info As following:
  • You will get an exercise sheet every week within your exercises class or via this web-page (see Exercise sheets).
  • Within the classes the exercises should be discussed within groups to get first drafts of ideas for solutions.
  • At home you should carefully write down full solutions in teams of 2 to 3 students.
  • The handing-in deadline can be found at the bottom of the exercise sheet.
  • After finishing your homework you drop it in the letter box in the basement of the MI-building, marked with the name of the course.
  • Please, write your full name and the number of your exercise class on your homework.
  • The corrected homework will be returned to you in the exercise class after the next.

question What happens if I did not pick my homework in the exercise class?
info Non-picked homework will be stored in the shelves at the entrance of the M9-finger till the end of the semester. Just pick them, if neccesary.

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.