On the implementation and strengthening of intersection cuts for QCQPs

• 成果类型: Article
• 署名作者: Chmiela, Antonia; Munoz, Gonzalo; Serrano, Felipe
• 署名单位: Zuse Institute Berlin; Universidad de O'Higgins
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01808-5
• 发表日期: 2023
• 页码: 549-586
• 关键词: minimal valid inequalities; convexity cuts; integer; PROGRAMS; sets

摘要

The generation of strong linear inequalities for QCQPs has been recently tackled by a number of authors using the intersection cut paradigm-a highly studied tool in integer programming whose flexibility has triggered these renewed efforts in non-linear settings. In this work, we consider intersection cuts using the recently proposed construction of maximal quadratic-free sets. Using these sets, we derive closed-form formulas to compute intersection cuts which allow for quick cut-computations by simply plugging-in parameters associated to an arbitrary quadratic inequality being violated by a vertex of an LP relaxation. Additionally, we implement a cut-strengthening procedure that dates back to Glover and evaluate these techniques with extensive computational experiments.