Advanced Integer Programming

This course covers advanced topics in the theory of integer linear and non-linear optimization. In particular we are interested in properties under which such problems 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.
• David, A.Cox, Johnm Little, DonalO'Shea: Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra (Chapters 1+2), Springer, 4th ed., 2015.

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 Prior knowledge in basic other areas might be beneficial but is not required.
Class Hours:	Tuesdays 16:00-18:00 and Thursdays 10:00-12:00
Room:	Seminarraum, Lennéstr. 2
Exams:	Oral exams, to be scheduled individually.

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Professor Dr. S. Held