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

Immanuel Bomze, Jianqiang Cheng, Peter James Clair Dickinson, Abdel Lisser

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
1 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)159-184
JournalMathematical programming
Volume166
Issue number1-2
DOIs
Publication statusPublished - Nov 2017

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