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Fundamentals of Convex Optimization (MA2504)


lecturer: Prof. Dr. Michael Ulbrich
learning assistant and organization: Dr. René Brandenberg

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


  • Jul, 22nd: Exam results given via TUMonline, post-exam review on Monday, 28th, 1pm.
  • Jul, 15th: Lecture notes updated.
  • Jul, 15th: Solution of the Multiple-Choice sheet 2 uploaded.
  • Jul, 13th: Multiple-Choice sheet 2 uploaded.
  • Jul, 7th: Lecture notes updated.
  • Jul, 3rd: Lecture notes updated.
  • Jun, 25th: Solution of the Multiple-Choice sheet 1 uploaded.
  • Jun, 5th: Multiple-Choice sheet 1 uploaded.
  • May, 29th: Lecture notes updated.
  • May, 12th: Lecture notes updated.
  • May, 5th: Due to the student plenum (SV) on Tuesday, 6th of May, 10-12 am exercise classes of groups 3 and 6 have to be canceled on that date. All students of this to groups are allowed to attend any of the other groups this week, except group 1.
  • Apr, 30th: Lecture notes updated.
  • Apr, 17th: Before anyone gets bored because of the easter holidays: I put a supplementary sheet for download. Only consider those supplementary sheets, if you are nosy, they are not relevant for the final exam.
  • Apr, 16th: New lecture room on thursdays: MW 1801!
  • Apr, 15th: Please hand in Sheet 1 until Monday, 28 th of april.
  • Apr, 14th: There will be no exercises in the week 21st to 25th of april. Thus sheet 2 start on 28th of april.
  • Apr, 3rd: From second week onward all lectures last 100 to 105 minutes (according to the schedule below), compensating lectures which have to be canceled.
  • Apr, 2nd: Lecture on Apr, 10th is canceled.
  • Apr, 2nd: First lecture on April, 7th, starting at 12.15. Exercise classes will start in the second week.
  • Apr, 2nd: Please contact Rene Brandenberg in his office (not via email), if none of the scheduled exercise hours fits with your semester schedule.

Dates of lectures/exercise classes and office hours

Type Day Time Room Teacher/Tutor Language Comment
Lecture 1 Monday 12:10 - 13:50 MI HS 1 Ulbrich english  
Lecture 2 Thursday 12:30 - 14:00 MW 1801 Ulbrich english  
Exercise class 1 Monday 16:00 - 18:00 02:04:011 Ghiglione english
Exercise class 2 Tuesday 08:15 - 10:00 02:04:011 Brandenberg german
Exercise class 3 Tuesday 10:15 - 12:00 02:04:011 Brandenberg german
Exercise class 4 Wednesday 10:15 - 12:00 02:04:011 Brandenberg german
Exercise class 5 Wednesday 12:15 - 14:00 02:04:011 Garreis german
Exercise class 6 Tuesday 10:15 - 12:00 02:08:011 Klöckner german
Exercise class 7 Monday 16:15 - 18:00 03:10:011 Klöckner 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. Michael Ulbrich tba
Dr. René Brandenberg on appointment
Viviana Ghiglione Thursday 11:00-12:00 (on 21 Dec. 2017 14:00--16:00 instead)

Lecture notes

Problem sheets

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

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

Multiple Choice Sheet 1(pdf) Multiple Choice Sheet 1 - Solution (pdf)
Multiple Choice Sheet 2(pdf) Multiple Choice Sheet 2 - Solution (pdf)

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.


  • 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
  • G. B. Dantzig, M. N. Thapa. Linear Programming 1: Introduction. Springer, 1997
  • P. Gritzmann: Grundlagen der mathematischen Optimierung, Springer, 2013
  • J.-B. Hiriart-Urruty, C. Lemarechal. Fundamentals of Convex Analysis. Springer, 2001
  • C. H. Papadimitriou, K. Steiglitz. Combinatorial Optimization: Algorithms and Complexity. Dover, 1998
  • R. T. Rockafellar. Convex Analysis. Princeton University Press, 1972
  • A. Schrijver. Theory of Linear and Integer Programming. Wiley, 1986
  • R. J. Vanderbei. Linear Programming, Foundations and Extensions. Springer, 2008


The exam takes place on 16th of July, 11.00-12.30 in MW 0001. It is a closed book examination.


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. Stefan Weltge
Discrete Mathematics

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


April 2018
Case Studies 2018: Save the date: Case Studies poster presentation on May 25th, 2018, final workshop on July 7th, 2018.