Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/4765
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dc.contributorDepartment of Applied Mathematics-
dc.creatorQi, L-
dc.creatorWan, Z-
dc.creatorYang, YF-
dc.date.accessioned2014-12-11T08:27:02Z-
dc.date.available2014-12-11T08:27:02Z-
dc.identifier.issn1052-6234-
dc.identifier.urihttp://hdl.handle.net/10397/4765-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2004 Society for Industrial and Applied Mathematicsen_US
dc.subjectGlobal optimizationen_US
dc.subjectNormal quartic polynomialen_US
dc.subjectTensoren_US
dc.titleGlobal minimization of normal quartic polynomials based on global descent directionsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage275-
dc.identifier.epage302-
dc.identifier.volume15-
dc.identifier.issue1-
dc.identifier.doi10.1137/S1052623403420857-
dcterms.abstractA normal quartic polynomial is a quartic polynomial whose fourth degree term coefficient tensor is positive definite. Its minimization problem is one of the simplest cases of nonconvex global optimization, and has engineering applications. We call a direction a global descent direction of a function at a point if there is another point with a lower function value along this direction. For a normal quartic polynomial, we present a criterion to find a global descent direction at a noncritical point, a saddle point, or a local maximizer. We give sufficient conditions to judge whether a local minimizer is global and give a method for finding a global descent direction at a local, but not global, minimizer. We also give a formula at a critical point and a method at a noncritical point to find a one-dimensional global minimizer along a global descent direction. Based upon these, we propose a global descent algorithm for finding a global minimizer of a normal quartic polynomial when n = 2. For the case n ≥ 3, we propose an algorithm for finding an ε-global minimizer. At each iteration of a second algorithm, a system of constrained nonlinear equations is solved. Numerical tests show that these two algorithms are promising.-
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on optimization, 2004, v. 15, no. 1, p. 275-302-
dcterms.isPartOfSIAM journal on optimization-
dcterms.issued2004-
dc.identifier.isiWOS:000226048600014-
dc.identifier.scopus2-s2.0-14944344547-
dc.identifier.eissn1095-7189-
dc.identifier.rosgroupidr29990-
dc.description.ros2005-2006 > Academic research: refereed > Publication in refereed journal-
dc.description.oaVersion of Recorden_US
dc.identifier.FolderNumberOA_IR/PIRAen_US
dc.description.pubStatusPublisheden_US
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