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Constraint selection in a build-up interior-point cutting-plane method for solving relaxations of the stable-set problem

Alexander Engau (), Miguel Anjos () and Immanuel Bomze

Mathematical Methods of Operations Research, 2013, vol. 78, issue 1, 35-59

Abstract: The stable-set problem is an NP-hard problem that arises in numerous areas such as social networking, electrical engineering, environmental forest planning, bioinformatics clustering and prediction, and computational chemistry. While some relaxations provide high-quality bounds, they result in very large and expensive conic optimization problems. We describe and test an integrated interior-point cutting-plane method that efficiently handles the large number of nonnegativity constraints in the popular doubly-nonnegative relaxation. This algorithm identifies relevant inequalities dynamically and selectively adds new constraints in a build-up fashion. We present computational results showing the significant benefits of this approach in comparison to a standard interior-point cutting-plane method. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Stable set; Maximum clique; Theta number; Semidefinite programming; Interior-point algorithms; Cutting-plane methods; Combinatorial optimization; 90C09; 90C20; 90C22; 90C27; 90C35; 90C51; 90C90 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00186-013-0431-z

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Handle: RePEc:spr:mathme:v:78:y:2013:i:1:p:35-59