Relaxations of mixed integer sets from lattice-free polyhedra

Alberto Del Pia () and Robert Weismantel ()
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Alberto Del Pia: University of Wisconsin-Madison
Robert Weismantel: ETH Zürich

Annals of Operations Research, 2016, vol. 240, issue 1, No 5, 95-117

Abstract: 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.

Keywords: Mixed integer programming; Cutting planes; Disjunctive programming; Lattice-free polyhedra (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10479-015-2024-0

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