401-3903-11L  Geometric Integer Programming

SemesterSpring Semester 2019
LecturersR. Weismantel, J. Paat, M. Schlöter
Periodicitynon-recurring course
Language of instructionEnglish

AbstractInteger programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
ObjectiveThe purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
ContentKey topics are:
- lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension,
- the theory of integral generating sets and its connection to totally dual integral systems,
- finite cutting plane algorithms based on lattices and integral generating sets.
Lecture notesnot available, blackboard presentation
LiteratureBertsimas, Weismantel: Optimization over Integers, Dynamic Ideas 2005.
Schrijver: Theory of linear and integer programming, Wiley, 1986.
Prerequisites / Notice"Mathematical Optimization" (401-3901-00L)