Fundamentals of Convex Optimization

Module MA2504

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA2504 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


convex sets, convex functions, projection, separation, subdifferential, optimality conditions, polyhedra, linear optimization problems, duality, (dual) simplex algorithm, Karush-Kuhn-Tucker conditions, selected applications and further topics of convex analysis and linear optimization

Learning Outcome

After successful completion of the module students are able to understand and apply the basic notions, concepts, and methods of convex analysis and linear optimization. Moreover, they are familiar with the underlying geometry and can model problems arising in practice.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, Vorteilhaft: MA2501 Algorithmic Discrete Mathematics, MA2503 Introduction to Nonlinear Optimization

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Fundamentals of Convex Optimization Gritzmann, P.
Mitwirkende: Klemm, F.
Montag, 16:15–17:45
Donnerstag, 08:15–09:45
Freitag, 14:00–15:30
UE 2 Fundamentals of Convex Optimization (Exercise Session) Gritzmann, P. Klemm, F. Termine in Gruppen

Learning and Teaching Methods

lecture, exercise module, assignments


blackboard, exercise sheets


P. Gritzmann. Grundlagen der mathematischen Optimierung, Springer, 2013. 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. 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, 1970. A. Schrijver. Theory of Linear and Integer Programming. Wiley, 1986. R. J. Vanderbei. Linear Programming, Foundations and Extensions, Springer, 2008.

Module Exam

Description of exams and course work


Exam Repetition

There is a possibility to take the exam at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Grundlagen der konvexen Optimierung
Mi, 12.10.2016, 8:00 bis 9:30 101
bis 19.9.2016 (Abmeldung bis 5.10.2016)

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