# 401-3903-11L Geometric Integer Programming

Semester | Spring Semester 2020 |

Lecturers | J. Paat |

Periodicity | non-recurring course |

Language of instruction | English |

Abstract | 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. |

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

Content | Key topics are: - Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension. - Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems - Duality theory for integer optimization problems from the vantage point of lattice free sets. |

Lecture notes | not available, blackboard presentation |

Literature | Lecture notes will be provided. Other helpful materials include Bertsimas, Weismantel: Optimization over Integers, 2005 and Schrijver: Theory of linear and integer programming, 1986. |

Prerequisites / Notice | "Mathematical Optimization" (401-3901-00L) |