Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/16215
DC FieldValueLanguage
dc.contributorDepartment of Applied Mathematics-
dc.creatorBomze, IM-
dc.creatorLing, C-
dc.creatorQi, L-
dc.creatorZhang, X-
dc.date.accessioned2014-12-19T06:54:05Z-
dc.date.available2014-12-19T06:54:05Z-
dc.identifier.issn0925-5001-
dc.identifier.urihttp://hdl.handle.net/10397/16215-
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.subjectBi-quartic optimizationen_US
dc.subjectOptimality conditionsen_US
dc.subjectPenalty functionen_US
dc.subjectPolynomial optimizationen_US
dc.subjectStandard simplexen_US
dc.titleStandard bi-quadratic optimization problems and unconstrained polynomial reformulationsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage663-
dc.identifier.epage687-
dc.identifier.volume52-
dc.identifier.issue4-
dc.identifier.doi10.1007/s10898-011-9710-5-
dcterms.abstractA so-called Standard Bi-Quadratic Optimization Problem (StBQP) consists in minimizing a bi-quadratic form over the Cartesian product of two simplices (so this is different from a Bi-Standard QP where a quadratic function is minimized over the same set). An application example arises in portfolio selection. In this paper we present a bi-quartic formulation of StBQP, in order to get rid of the sign constraints. We study the first- and second-order optimality conditions of the original StBQP and the reformulated bi-quartic problem over the product of two Euclidean spheres. Furthermore, we discuss the one-to-one correspondence between the global/local solutions of StBQP and the global/local solutions of the reformulation. We introduce a continuously differentiable penalty function. Based upon this, the original problem is converted into the problem of locating an unconstrained global minimizer of a (specially structured) polynomial of degree eight.-
dcterms.bibliographicCitationJournal of global optimization, 2012, v. 52, no. 4, p. 663-687-
dcterms.isPartOfJournal of global optimization-
dcterms.issued2012-
dc.identifier.isiWOS:000301841300001-
dc.identifier.scopus2-s2.0-84886729967-
dc.identifier.eissn1573-2916-
dc.identifier.rosgroupidr64096-
dc.description.ros2012-2013 > Academic research: refereed > Publication in refereed journal-
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