Relaxations of mixed integer sets from lattice-free polyhedra

Relaxations of mixed integer sets from lattice-free polyhedra

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Article ID: iaor20162273
Volume: 240
Issue: 1
Start Page Number: 95
End Page Number: 117
Publication Date: May 2016
Journal: Annals of Operations Research
Authors: ,
Keywords: combinatorial optimization, programming: integer, heuristics
Abstract:

This paper gives an introduction to a recently established link between the geometry of numbers and mixed integer optimization. The main focus is to provide a review of families of lattice‐free polyhedra and their use in a disjunctive programming approach. The use of lattice‐free polyhedra in the context of deriving and explaining cutting planes for mixed integer programs is not only mathematically interesting, but it leads to some fundamental new discoveries, such as an understanding under which conditions cutting planes algorithms converge finitely.

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