Mathematical Programming & Combinatorial Optimization

This is a master-level course focusing on two topics in combinatorial optimization: i) structure of polytopes and the complexity of their description, ii) efficient methods for optimization over polytopes (and polyhedra).

Organization

During the Summer Semester 2025-2026 the lectures are scheduled on Wednesdays at 10:40 in S221 (KAM corridor 2nd floor) in Mala Strana.

Course Requirements (Exam etc.)

The final grade for the course will be based on an exam at the end of the semester. You obtain course credit you need to do a project. Check the details here.

Tentative Syllabus

Polyhedra/Polytopes: basic notions, face lattice, polar duality
Ellipsoid algorithm for linear programming
Interior point methods for linear programming
Extended formulations

The following is a list of Books and other material relevant to the lectures. The list will be updated as needed.

Textbook Lectures on Polytopes by Guenter M. Ziegler - available in the University library at Mala Strana.
Lecture notes on the ellipsoid algorithm by M. Goemans
Lecture notes on interior point method by M. Goemans (see chapter 13)
Textbook Linear Programming by Howard Karloff, chapters 4 and 5 - available in the University library at Mala Strana.
Lecture notes on polynomial time LP algorithms by P. Kolman (in Czech)