Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000100008 |
Resumo: | An alternative strategy to solve the subproblems of the Method of Moving Asymptotes (MMA) is presented, based on a trust-region scheme applied to the dual of the MMA subproblem. At each iteration, the objective function of the dual problem is approximated by a regularized spectral model. A globally convergent modification to the MMA is also suggested, in which the conservative condition is relaxed by means of a summable controlled forcing sequence. Another modification to the MMA previously proposed by the authors [Optim. Methods Softw., 25 (2010), pp. 883-893] is recalled to be used in the numerical tests. This modification is based on the spectral parameter for updating the MMA models, so as to improve their quality. The performed numerical experiments confirm the efficiency of the indicated modifications, especially when jointly combined. |
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Computational & Applied Mathematics |
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Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region schemenonlinear programmingMethod of Moving Asymptotesspectral parameterglobal convergencedual problemAn alternative strategy to solve the subproblems of the Method of Moving Asymptotes (MMA) is presented, based on a trust-region scheme applied to the dual of the MMA subproblem. At each iteration, the objective function of the dual problem is approximated by a regularized spectral model. A globally convergent modification to the MMA is also suggested, in which the conservative condition is relaxed by means of a summable controlled forcing sequence. Another modification to the MMA previously proposed by the authors [Optim. Methods Softw., 25 (2010), pp. 883-893] is recalled to be used in the numerical tests. This modification is based on the spectral parameter for updating the MMA models, so as to improve their quality. The performed numerical experiments confirm the efficiency of the indicated modifications, especially when jointly combined.Sociedade Brasileira de Matemática Aplicada e Computacional2011-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000100008Computational & Applied Mathematics v.30 n.1 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000100008info:eu-repo/semantics/openAccessGomes-Ruggiero,Márcia A.Sachine,MaelSantos,Sandra A.eng2011-03-22T00:00:00Zoai:scielo:S1807-03022011000100008Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2011-03-22T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
title |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
spellingShingle |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme Gomes-Ruggiero,Márcia A. nonlinear programming Method of Moving Asymptotes spectral parameter global convergence dual problem |
title_short |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
title_full |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
title_fullStr |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
title_full_unstemmed |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
title_sort |
Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme |
author |
Gomes-Ruggiero,Márcia A. |
author_facet |
Gomes-Ruggiero,Márcia A. Sachine,Mael Santos,Sandra A. |
author_role |
author |
author2 |
Sachine,Mael Santos,Sandra A. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Gomes-Ruggiero,Márcia A. Sachine,Mael Santos,Sandra A. |
dc.subject.por.fl_str_mv |
nonlinear programming Method of Moving Asymptotes spectral parameter global convergence dual problem |
topic |
nonlinear programming Method of Moving Asymptotes spectral parameter global convergence dual problem |
description |
An alternative strategy to solve the subproblems of the Method of Moving Asymptotes (MMA) is presented, based on a trust-region scheme applied to the dual of the MMA subproblem. At each iteration, the objective function of the dual problem is approximated by a regularized spectral model. A globally convergent modification to the MMA is also suggested, in which the conservative condition is relaxed by means of a summable controlled forcing sequence. Another modification to the MMA previously proposed by the authors [Optim. Methods Softw., 25 (2010), pp. 883-893] is recalled to be used in the numerical tests. This modification is based on the spectral parameter for updating the MMA models, so as to improve their quality. The performed numerical experiments confirm the efficiency of the indicated modifications, especially when jointly combined. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01 |
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=S1807-03022011000100008 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000100008 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022011000100008 |
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 |
Computational & Applied Mathematics v.30 n.1 2011 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
_version_ |
1754734890235985920 |