Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/4765
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | - |
dc.creator | Qi, L | - |
dc.creator | Wan, Z | - |
dc.creator | Yang, YF | - |
dc.date.accessioned | 2014-12-11T08:27:02Z | - |
dc.date.available | 2014-12-11T08:27:02Z | - |
dc.identifier.issn | 1052-6234 | - |
dc.identifier.uri | http://hdl.handle.net/10397/4765 | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | © 2004 Society for Industrial and Applied Mathematics | en_US |
dc.subject | Global optimization | en_US |
dc.subject | Normal quartic polynomial | en_US |
dc.subject | Tensor | en_US |
dc.title | Global minimization of normal quartic polynomials based on global descent directions | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 275 | - |
dc.identifier.epage | 302 | - |
dc.identifier.volume | 15 | - |
dc.identifier.issue | 1 | - |
dc.identifier.doi | 10.1137/S1052623403420857 | - |
dcterms.abstract | A 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.accessRights | open access | en_US |
dcterms.bibliographicCitation | SIAM journal on optimization, 2004, v. 15, no. 1, p. 275-302 | - |
dcterms.isPartOf | SIAM journal on optimization | - |
dcterms.issued | 2004 | - |
dc.identifier.isi | WOS:000226048600014 | - |
dc.identifier.scopus | 2-s2.0-14944344547 | - |
dc.identifier.eissn | 1095-7189 | - |
dc.identifier.rosgroupid | r29990 | - |
dc.description.ros | 2005-2006 > Academic research: refereed > Publication in refereed journal | - |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | OA_IR/PIRA | en_US |
dc.description.pubStatus | Published | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
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Qi_Global_minimization_normal.pdf | 360.14 kB | Adobe PDF | View/Open |
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