Spectral projected gradient method for the procrustes problem

Detalhes bibliográficos
Autor(a) principal: Francisco,J.B.
Data de Publicação: 2014
Outros Autores: Martini,T.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000100008
Resumo: We study and analyze a nonmonotone globally convergent method for minimization onclosed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD "with inaccuracy" to improve the performance of the algorithm, since the solution of the subproblem by traditional techniques, which is required in each iteration, is computationally expensive. Other feasible methods are mentioned,including a curvilinear search algorithm and a minimization along geodesics algorithm. Finally, we illustrate the numerical performance of the methods when applied to the Orthogonal Procrustes Problem.
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spelling Spectral projected gradient method for the procrustes problemorthogonality constraintsnonmonotone algorithmOrthogonal Procrustes ProblemSpectral Projected Gradient MethodWe study and analyze a nonmonotone globally convergent method for minimization onclosed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD "with inaccuracy" to improve the performance of the algorithm, since the solution of the subproblem by traditional techniques, which is required in each iteration, is computationally expensive. Other feasible methods are mentioned,including a curvilinear search algorithm and a minimization along geodesics algorithm. Finally, we illustrate the numerical performance of the methods when applied to the Orthogonal Procrustes Problem.Sociedade Brasileira de Matemática Aplicada e Computacional2014-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000100008TEMA (São Carlos) v.15 n.1 2014reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2014.015.01.0083info:eu-repo/semantics/openAccessFrancisco,J.B.Martini,T.eng2014-06-10T00:00:00Zoai:scielo:S2179-84512014000100008Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2014-06-10T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Spectral projected gradient method for the procrustes problem
title Spectral projected gradient method for the procrustes problem
spellingShingle Spectral projected gradient method for the procrustes problem
Francisco,J.B.
orthogonality constraints
nonmonotone algorithm
Orthogonal Procrustes Problem
Spectral Projected Gradient Method
title_short Spectral projected gradient method for the procrustes problem
title_full Spectral projected gradient method for the procrustes problem
title_fullStr Spectral projected gradient method for the procrustes problem
title_full_unstemmed Spectral projected gradient method for the procrustes problem
title_sort Spectral projected gradient method for the procrustes problem
author Francisco,J.B.
author_facet Francisco,J.B.
Martini,T.
author_role author
author2 Martini,T.
author2_role author
dc.contributor.author.fl_str_mv Francisco,J.B.
Martini,T.
dc.subject.por.fl_str_mv orthogonality constraints
nonmonotone algorithm
Orthogonal Procrustes Problem
Spectral Projected Gradient Method
topic orthogonality constraints
nonmonotone algorithm
Orthogonal Procrustes Problem
Spectral Projected Gradient Method
description We study and analyze a nonmonotone globally convergent method for minimization onclosed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD "with inaccuracy" to improve the performance of the algorithm, since the solution of the subproblem by traditional techniques, which is required in each iteration, is computationally expensive. Other feasible methods are mentioned,including a curvilinear search algorithm and a minimization along geodesics algorithm. Finally, we illustrate the numerical performance of the methods when applied to the Orthogonal Procrustes Problem.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000100008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000100008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2014.015.01.0083
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.15 n.1 2014
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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