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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


  • Jul, 24th: The exam takes place completely in MW 2001. Please, noboby should go to MI HS1.
  • Jul, 22nd: The Multiple Choice sheet is relaunched.
  • Jul, 20th: The online version of the Multiple Choice sheet had an error, so we removed it. We hope we can repair it until monday noon. So far you may use the downloadable pdf-version.
  • Jul, 15th: In den Ferien wird es ein Computerpraktikum zur Linearen Optimierung geben, in dem die Theorie aus der Vorlesung praktisch anhand von Programmieraufgaben angewendet wird.
  • Jun, 3rd: Lectures on June 7th and 10th are canceled.
  • May, 27th: Because of the extremly low attendance, Exercise-class 8 was canceled for the rest of the semester.
  • Apr, 29th: Because of the public holiday on wednesday, there will be replacement groups tomorrow, tuesday 30th, 10.15-12.00 am in 02.06.020 and on thursday 2nd, 4.00-5.45 p, in 02.06.020. Please mind the following: Only students registered for group 2 should attend the exercis group at 10.15 am tommorow, all others who want to attend the exercises tomorrow, 10.15 am should go to room 02.06.020. Thanks.
  • Apr, 26th: The cover sheet is online now.
  • Apr, 18th: The exercise classes of group 3 and 8 on April, 24th are postponed to the 25th, 4-6pm because of the FVV. Anyone who is not able to attend the class on thursday may visit any other class that week. The week after exercise classes of group 3,4,7, and 8 are postponed to the 2nd of May, 4-6pm because of the public holiday on the 1st. Again you may also visit any of the tuesday or friday groups in that week.
  • Apr, 8th: First lecture on April, 15th. Exercise classes will start in the second week.

Dates of lectures/exercise classes and office hours

Type Day Time Room Teacher/Tutor Language Comment
Lecture 1 Monday 12:00 - 14:00 MI HS 1 Gritzmann english  
Lecture 2 Friday 14:00 - 16:00 MI HS 2 Gritzmann english  
Exercise class 1 Tuesday 8:15 - 10:00 00:09:022 Brandenberg german  
Exercise class 2 Tuesday 10:15 - 12:00 02:08:011 Brandenberg german  
Exercise class 3 Wednesday 10:15 - 12:00 02:09:014 Huang german  
Exercise class 4 Wednesday 12:15 - 14:00 03:10:011 Ghiglione english  
Exercise class 5 canceled
Exercise class 6 Friday 12:00 - 13:45 03:10:011 Brandenberg german  
Exercise class 7 Wednesday 12:15 - 14:00 MW 0234 Huang german  
Exercise class 8 canceled

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 (see below for details).

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
Viviana Ghiglione Thursday 11:00-12:00 (on 21 Dec. 2017 14:00--16:00 instead)
Wei Huang by appointment

Lecture notes

Problem sheets

Problem sheets Comments Solution outlines Supplementary sheets (voluntary) Comments
Sheet 01   Solution outlines 01 Supplementary sheet 01
Sheet 02   Solution outlines 02  
Sheet 03   Solution outlines 03 Supplementary sheet 03
Sheet 04   Solution outlines 04  
Sheet 05   Solution outlines 05  
Sheet 06   Solution outlines 06  
Sheet 07   Solution outlines 07 Supplementary sheet 07
Sheet 08   Solution outlines 08  
Sheet 09   Solution outlines 09  
Sheet 10   Solution outlines 10  
Sheet 11   Solution outlines 11 Supplementary sheet 11
Sheet 12   Solution outlines 12 Supplementary sheet 12 Table heads corrected !
Sheet 13   Solution outlines 13

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

Multiple Choice Sheet (online)
Multiple Choice Sheet (pdf) Multiple Choice Sheet - Solution (pdf)

Grade boni for homework participation (Notenbonus)

For the continuos 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.


  • P. Gritzmann: Grundlagen der mathematischen Optimierung, Springer, 2013

  • 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
  • D. Bertsimas, J. N. Tsitsiklis. Introduction to Linear Optimization, Athena Scientific, 1997
  • T. Bonnesen, W. Fenchel: Theorie der konvexen Körper (korr. Nachdruck), Springer, 1974
  • G. B. Dantzig, M. N. Thapa. Linear Programming 1: Introduction. Springer, 1997
  • C. Geiger, C. Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002
  • P.E. Gill, W. Murray, M.H. Wright: Practical Optimization, Academic Press, 1981
  • B. Grünbaum: Polytopes, Springer, 1993
  • J.-B. Hiriart-Urruty, C. Lemarechal. Fundamentals of Convex Analysis. Springer, 2001
  • F. Jarre, J. Stoer: Optimierung, Springer, 2004
  • M. Minoux: Mathematical Programming: Theory and Algorithms, Wiley, 1986
  • C. H. Papadimitriou, K. Steiglitz. Combinatorial Optimization: Algorithms and Complexity. Dover, 1998
  • 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
  • A. Schrijver. Theory of Linear and Integer Programming. Wiley, 1986 -->
  • 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 TUMonlin. Mind the deadlines given in TUMonline!
  • First, there will only be the exersise classes already listet under Dates of lectures/exercise classes and office hours. In each of the classes a given maximum 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.

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

question Am I automatically signed in the repetition exam if I failed the first?
info No.

question How does the Homework system works for this 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 to 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.