Active-set strategy in Powell's method for optimization without derivatives

Autores
Arouxét, María Belén; Echebest, Nélida Ester; Pilotta, Elvio Ángel
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method 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 implementation 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. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc/3.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/40173

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repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Active-set strategy in Powell's method for optimization without derivativesArouxét, María BelénEchebest, Nélida EsterPilotta, Elvio ÁngelCiencias ExactasMatemáticaactive-set methodderivative-free optimizationspectral gradient methodIn this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method 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 implementation 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. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.Facultad de Ciencias Exactas2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf171-196http://sedici.unlp.edu.ar/handle/10915/40173enginfo:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/09.pdfinfo:eu-repo/semantics/altIdentifier/issn/0101-8205info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/3.0/Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T10:57:04Zoai:sedici.unlp.edu.ar:10915/40173Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 10:57:04.301SEDICI (UNLP) - Universidad Nacional de La Platafalse
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, María Belén
Ciencias Exactas
Matemática
active-set method
derivative-free optimization
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
dc.creator.none.fl_str_mv Arouxét, María Belén
Echebest, Nélida Ester
Pilotta, Elvio Ángel
author Arouxét, María Belén
author_facet Arouxét, María Belén
Echebest, Nélida Ester
Pilotta, Elvio Ángel
author_role author
author2 Echebest, Nélida Ester
Pilotta, Elvio Ángel
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
topic Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
dc.description.none.fl_txt_mv In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method 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 implementation 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. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
Facultad de Ciencias Exactas
description In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method 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 implementation 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. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
publishDate 2011
dc.date.none.fl_str_mv 2011
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format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/40173
url http://sedici.unlp.edu.ar/handle/10915/40173
dc.language.none.fl_str_mv eng
language eng
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info:eu-repo/semantics/altIdentifier/issn/0101-8205
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/3.0/
Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc/3.0/
Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)
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171-196
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instname:Universidad Nacional de La Plata
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instname_str Universidad Nacional de La Plata
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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