Geometric Integer Programming

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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.


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.


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