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

Autores
Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel
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 [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 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.
Fil: Arouxet, Maria Belen. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Echebest, Nélida Ester. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Pilotta, Elvio Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba; Argentina
Materia
derivative-free optimization
active-set method
spectral gradient method
polinomial interpolation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/193948
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/193948
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Active-set strategy in Powell's method for optimization without derivativesArouxet, Maria BelenEchebest, Nélida EsterPilotta, Elvio Angelderivative-free optimizationactive-set methodspectral gradient methodpolinomial interpolationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 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 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.Fil: Arouxet, Maria Belen. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Echebest, Nélida Ester. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Pilotta, Elvio Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba; ArgentinaSociedade Brasileira de Matemática Aplicada e Computacional2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/193948Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Active-set strategy in Powell's method for optimization without derivatives; Sociedade Brasileira de Matemática Aplicada e Computacional; Computational And Applied Mathematics; 30; 1; 1-2011; 171-1960101-8205CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.scielo.br/j/cam/a/GwBm3thcKBWgzMM3TRg968b/?lang=eninfo:eu-repo/semantics/altIdentifier/doi/10.1590/S1807-03022011000100009info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:34:42Zoai:ri.conicet.gov.ar:11336/193948instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:34:42.873CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
Arouxet, Maria Belen
derivative-free optimization
active-set method
spectral gradient method
polinomial interpolation
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 Arouxet, Maria Belen
Echebest, Nélida Ester
Pilotta, Elvio Angel
author Arouxet, Maria Belen
author_facet Arouxet, Maria Belen
Echebest, Nélida Ester
Pilotta, Elvio Angel
author_role author
author2 Echebest, Nélida Ester
Pilotta, Elvio Angel
author2_role author
author
dc.subject.none.fl_str_mv derivative-free optimization
active-set method
spectral gradient method
polinomial interpolation
topic derivative-free optimization
active-set method
spectral gradient method
polinomial interpolation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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 [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 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.
Fil: Arouxet, Maria Belen. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Echebest, Nélida Ester. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Pilotta, Elvio Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba; Argentina
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 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.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/193948
Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Active-set strategy in Powell's method for optimization without derivatives; Sociedade Brasileira de Matemática Aplicada e Computacional; Computational And Applied Mathematics; 30; 1; 1-2011; 171-196
0101-8205
CONICET Digital
CONICET
url http://hdl.handle.net/11336/193948
identifier_str_mv Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Active-set strategy in Powell's method for optimization without derivatives; Sociedade Brasileira de Matemática Aplicada e Computacional; Computational And Applied Mathematics; 30; 1; 1-2011; 171-196
0101-8205
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.scielo.br/j/cam/a/GwBm3thcKBWgzMM3TRg968b/?lang=en
info:eu-repo/semantics/altIdentifier/doi/10.1590/S1807-03022011000100009
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
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 reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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