Monoidal strengthening and unique lifting in MIQCPs

• 成果类型: Article
• 署名作者: Chmiela, Antonia; Munoz, Gonzalo; Serrano, Felipe
• 署名单位: Zuse Institute Berlin; Universidad de Chile
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-024-02112-0
• 发表日期: 2025
• 页码: 189-222
• 关键词: integer variables; cuts; sets

摘要

Using the recently proposed maximal quadratic-free sets and the well-known monoidal strengthening procedure, we show how to improve intersection cuts for quadratically-constrained optimization problems by exploiting integrality requirements. We provide an explicit construction that allows an efficient implementation of the strengthened cuts along with computational results showing their improvements over the standard intersection cuts. We also show that, in our setting, there is unique lifting which implies that our strengthening procedure is generating the best possible cut coefficients for the integer variables.