Facet separation with one linear program

• 成果类型: Article
• 署名作者: Conforti, Michele; Wolsey, Laurence A.
• 署名单位: University of Padua; Universite Catholique Louvain
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1299-8
• 发表日期: 2019
• 页码: 361-380
• 关键词: lift-and-project; inequalities

摘要

Given polyhedron P and and a point x* the separation problem for polyhedra asks to certify that x* is an element of P and if not, to determine an inequality that is satisfied by P and violated by x*. This problem is repeatedly solved in cutting plane methods for Integer Programming and the quality of the violated inequality is an essential feature in the performance of such methods. In this paper we address the problem of finding efficiently an inequality that is violated by x and either defines an improper face or a facet of P. We show that, by solving a single linear program, one almost surely obtains such an improper face or facet.