Relaxations of mixed integer sets from lattice‐free polyhedra

Relaxations of mixed integer sets from lattice‐free polyhedra

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Article ID: iaor20125331
Volume: 10
Issue: 3
Start Page Number: 221
End Page Number: 244
Publication Date: Sep 2012
Journal: 4OR
Authors: ,
Keywords: optimization
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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