Reference : An analysis of mixed integer linear sets based on lattice point free convex sets
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/35087
An analysis of mixed integer linear sets based on lattice point free convex sets
English
Andersen, Kent [Otto-von-Guericke Universität Magdeburg > Institut für Mathematische Optimierung > > >]
Louveaux, Quentin mailto [Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Optimisation discrète >]
Weismantel, Robert [Otto-von-Guericke Universituat Magdeburg > Institut für Mathematische Optimierung > > >]
Feb-2010
Mathematics of Operations Research
Institute for Operations Research (INFORMS)
35
1
233-256
Yes (verified by ORBi)
International
0364-765X
1526-5471
[en] mixed-integer sets ; lattice-point-free polyhedra ; cutting planes
[en] The set obtained by adding all cuts whose validity follows from a maximal lattice free polyhedron with max-facet-width at most w is called the w th split closure. We show the w th split closure is a polyhedron. This generalizes a previous result showing this to be true when w = 1. We also consider the design of finite cutting plane proofs for the validity of an inequality. Given a measure of “size” of a maximal lattice free polyhedron, a natural question is how large a size s of a maximal lattice free polyhedron is required to design a finite cutting plane proof for the validity of an inequality. We characterize s based on the faces of the linear relaxation of the mixed integer linear set.
http://hdl.handle.net/2268/35087
10.1287/moor.1090.0439

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