On the Rank of Disjunctive Cuts

Authors:
Alberto Del Pia
Affiliations:
Institute for Operations Research, Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
Venue:
Mathematics of Operations Research
Year:
2012

Citing 7
Cited 0

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Abstract

Let L be a family of lattice-free polyhedra in Rm containing the splits. Given a polyhedron P in Rm + n, we characterize when a valid inequality for P ∩ (Zm × Rn) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L for every polyhedron P. Our results imply interesting consequences, related to split rank and to integral lattice-free polyhedra, that extend recent research findings.