Advanced Integer Programming

This course covers advanced topics in the theory of integer linear and non-linear optimization. We will start with studying cutting plane methods that are used for solving real-world integer problems such as the traveling salesperson problem. Then we look deeper into the theory, and study under which conditions integer programs can be solved or approximated efficiently. Thereby we will study connections to other fields of mathematics such as the geometry of numbers and algebraic geometry.

This course will be in English and based on topics from several books, as well as recent research papers. Recommended books (available in our library):

• D. Bertsimas, R: Weismantel: Optimization over Integers, Dynamic Ideas, 2005.
• J.A De Loera, R. Hemmecke, M. Köppe: Algebraic and Geometric Ideas in the Theory of Discrete Optimization, MOS-SIAM Series on Optimization, 2012.
• A. Schrijver: Theory of Linear and Integer Programming, Wiley, New York, 1986.
• M. Conforti, G. Cornuéjols, G. Zambelli: Integer Programming, Springer International Publishing, 2014.
• D.A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 5th edition, 2024.

Prerequisites:	Linear and Integer Optimization (F4C1) in particular basic knowledge on linear and integer programming, NP-completeness see, e.g., Chapters 3-5 and 15.3 of the Korte-Vygen textbook. I will also provide access to my lecture notes on Linear and Integer Programming Prior knowledge in basic other areas might be beneficial but is not required.
Class Hours:	Tuesdays and Thursdays 16:15-18:00
Room:	Seminarraum, Lennéstr. 2
Exams:	Oral exams, to be scheduled individually.

---

Professor Dr. S. Held