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 2024-2025 the lectures are scheduled on Thursdays at 09:00 in S6 in Mala Strana. Tutorials are held immediately preceding the lecture in the same room at 8:15.

Course Requirements (Exam etc.)

The final grade for the course will be based on an exam at the end of the semester. You must obtain a "pass" in the tutorial to be able to take the exam for this course. .

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)