Active-set strategy in Powell's method for optimization without derivatives
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=S1807-03022011000100009 |
Resumo: | In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method [38] for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective function is constructed around the current iterate and this model is minimized to obtain a new trial point. The whole process is embedded within a trust-region framework. Our algorithm uses infinity norm instead of the Euclidean norm and we solve a box constrained quadratic subproblem using an active-set strategy to explore faces of the box. Therefore, a bound constrained optimization algorithm is easily extended. We compare our im_ plementation with NEWUOA and BOBYQA, Powell's algorithms for unconstrained and bound constrained derivative free optimization respectively. Numerical experiments show that, in general, our algorithm require less functional evaluations than Powell's algorithms. |
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Computational & Applied Mathematics |
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Active-set strategy in Powell's method for optimization without derivativesderivative-free optimizationactive-set methodspectral gradient methodIn this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method [38] for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective function is constructed around the current iterate and this model is minimized to obtain a new trial point. The whole process is embedded within a trust-region framework. Our algorithm uses infinity norm instead of the Euclidean norm and we solve a box constrained quadratic subproblem using an active-set strategy to explore faces of the box. Therefore, a bound constrained optimization algorithm is easily extended. We compare our im_ plementation with NEWUOA and BOBYQA, Powell's algorithms for unconstrained and bound constrained derivative free optimization respectively. Numerical experiments show that, in general, our algorithm require less functional evaluations than Powell's algorithms.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=S1807-03022011000100009Computational & Applied Mathematics v.30 n.1 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000100009info:eu-repo/semantics/openAccessArouxét,Ma. BelénEchebest,NélidaPilotta,Elvio A.eng2011-03-22T00:00:00Zoai:scielo:S1807-03022011000100009Revistahttps://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 |
Active-set strategy in Powell's method for optimization without derivatives |
title |
Active-set strategy in Powell's method for optimization without derivatives |
spellingShingle |
Active-set strategy in Powell's method for optimization without derivatives Arouxét,Ma. Belén derivative-free optimization active-set method spectral gradient method |
title_short |
Active-set strategy in Powell's method for optimization without derivatives |
title_full |
Active-set strategy in Powell's method for optimization without derivatives |
title_fullStr |
Active-set strategy in Powell's method for optimization without derivatives |
title_full_unstemmed |
Active-set strategy in Powell's method for optimization without derivatives |
title_sort |
Active-set strategy in Powell's method for optimization without derivatives |
author |
Arouxét,Ma. Belén |
author_facet |
Arouxét,Ma. Belén Echebest,Nélida Pilotta,Elvio A. |
author_role |
author |
author2 |
Echebest,Nélida Pilotta,Elvio A. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Arouxét,Ma. Belén Echebest,Nélida Pilotta,Elvio A. |
dc.subject.por.fl_str_mv |
derivative-free optimization active-set method spectral gradient method |
topic |
derivative-free optimization active-set method spectral gradient method |
description |
In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method [38] for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective function is constructed around the current iterate and this model is minimized to obtain a new trial point. The whole process is embedded within a trust-region framework. Our algorithm uses infinity norm instead of the Euclidean norm and we solve a box constrained quadratic subproblem using an active-set strategy to explore faces of the box. Therefore, a bound constrained optimization algorithm is easily extended. We compare our im_ plementation with NEWUOA and BOBYQA, Powell's algorithms for unconstrained and bound constrained derivative free optimization respectively. Numerical experiments show that, in general, our algorithm require less functional evaluations than Powell's algorithms. |
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=S1807-03022011000100009 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000100009 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022011000100009 |
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_ |
1754734890237034496 |