On the accuracy of uniform polyhedral approximations of the copositive cone

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dc.citation.epage173en_US
dc.citation.issueNumber1en_US
dc.citation.spage155en_US
dc.citation.volumeNumber27en_US
dc.contributor.authorYıldırım, A.en_US
dc.date.accessioned2016-02-08T09:48:40Z
dc.date.available2016-02-08T09:48:40Z
dc.date.issued2012en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. We propose a hierarchy of increasingly better outer polyhedral approximations to the copositive cone. We establish that the sequence of approximations is exact in the limit. By combining our outer polyhedral approximations with the inner polyhedral approximations due to de Klerk and Pasechnik [SIAM J. Optim. 12 (2002), pp. 875-892], we obtain a sequence of increasingly sharper lower and upper bounds on the optimal value of a copositive program. Under primal and dual regularity assumptions, we establish that both sequences converge to the optimal value. For standard quadratic optimization problems, we derive tight bounds on the gap between the upper and lower bounds. We provide closed-form expressions of the bounds for the maximum stable set problem. Our computational results shed light on the quality of the bounds on randomly generated instances.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:48:40Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2012en
dc.identifier.doi10.1080/10556788.2010.540014en_US
dc.identifier.eissn1029-4937
dc.identifier.issn1055-6788
dc.identifier.urihttp://hdl.handle.net/11693/21605
dc.language.isoEnglishen_US
dc.publisherTaylor & Francisen_US
dc.relation.isversionofhttp://dx.doi.org/10.1080/10556788.2010.540014en_US
dc.source.titleOptimization Methods and Softwareen_US
dc.subjectCopositive coneen_US
dc.subjectCompletely positive coneen_US
dc.subjectConic optimizationen_US
dc.subjectStandard quadratic optimizationen_US
dc.subjectOptimization problemsen_US
dc.titleOn the accuracy of uniform polyhedral approximations of the copositive coneen_US
dc.typeArticleen_US

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