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

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作者
Alexander Engau
Miguel F. Anjos
Immanuel Bomze
机构
[1] University of Colorado Denver,
[2] GERAD & École Polytechnique de Montréal,undefined
[3] University of Vienna,undefined
关键词
Stable set; Maximum clique; Theta number; Semidefinite programming; Interior-point algorithms; Cutting-plane methods; Combinatorial optimization; 90C09; 90C20; 90C22; 90C27; 90C35; 90C51; 90C90;
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摘要
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.
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页码:35 / 59
页数:24
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