401-3901-00L Mathematical Optimization
|Semester||Autumn Semester 2020|
|Periodicity||yearly recurring course|
|Language of instruction||English|
|Abstract||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.|