On the Rank of Disjunctive Cuts

• 成果类型: Article
• 署名作者: Del Pia, Alberto
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1110.0527
• 发表日期: 2012
• 页码: 372-378
• 关键词: intersection cuts; split closure

摘要

Let L be a family of lattice-free polyhedra in R-m containing the splits. Given a polyhedron P in Rm+n, we characterize when a valid inequality for P boolean AND (Z(n) x R-n) 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.