Geometric Integer Programming

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Lecturer Assistant Lecture Exercise
Prof. Dr. Robert Weismantel

Jörg Bader,

Kevin Zemmer

Thu 13-15

HG G 26.3

Wed 11-12

HG F 26.3

Short description

Integer 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.
The purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.


"Mathematical Optimization" (401-3901-00L).


Key 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.


The weekly exercise sheets for Geometric Integer Programming can be found at the following moodle course:
All information on the course can be found there. The moodle course is regularly updated and may also be accessed as a guest.


- Bertsimas, Weismantel: Optimization over Integers, Dynamic Ideas 2005,
- Schrijver: Theory of linear and integer programming, Wiley, 1986.


The final exam is oral.


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