A fresh CP look at mixed-binary QPs: new formulations and relaxations

• 成果类型: Article
• 署名作者: Bomze, Immanuel M.; Cheng, Jianqiang; Dickinson, Peter J. C.; Lisser, Abdel
• 署名单位: University of Vienna; University of Arizona; University of Twente; Universite Paris Saclay
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1109-8
• 发表日期: 2017
• 页码: 159-184
• 关键词: quadratic optimization problems; copositive optimization; REPRESENTATION; PROGRAMS; rank; cone

摘要

Triggered by Burer's seminal characterization from 2009, many copositive reformulations of mixed-binary QPs have been discussed by now. Most of them can be used as proper relaxations, if the intractable co(mpletely)positive cones are replaced by tractable approximations. While the widely used approximation hierarchies have the disadvantage to use positive-semidefinite (psd) matrices of orders which rapidly increase with the level of approximation, alternatives focus on the problem of keeping psd matrix orders small, with the aim to avoid memory problems in the interior point algorithms. This work continues this approach, proposing new reformulations and relaxations. Moreover, we provide a thorough comparison of the respective duals and establish a monotonicity relation among their duality gaps. We also identify sufficient conditions for strong duality/zero duality gap in some of these formulations and generalize some of our observations to general conic problems.