Mathematical treatment of diverse optimization techniques.
Objective
The goal of this course is to get a thorough understanding of various classical mathematical optimization techniques with an emphasis on polyhedral approaches. In particular, we want students to develop a good understanding of some important problem classes in the field, of structural mathematical results linked to these problems, and of solution approaches based on this structural understanding.
Content
Key topics include: - Linear programming and polyhedra; - Flows and cuts; - Combinatorial optimization problems and techniques; - Equivalence between optimization and separation; - Brief introduction to Integer Programming.
Literature
- Bernhard Korte, Jens Vygen: Combinatorial Optimization. 6th edition, Springer, 2018. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003. This work has 3 volumes. - Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993. - Alexander Schrijver: Theory of Linear and Integer Programming. John Wiley, 1986.
Prerequisites / Notice
Solid background in linear algebra.
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
written 180 minutes
Additional information on mode of examination
Credits can only be recognized for either "Mathematical Optimization" or for the previously offered course "Combinatorial Optimization" (401-4904-00L), but not both.
Written aids
None
This information can be updated until the beginning of the semester; information on the examination timetable is binding.