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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/40173
Ver los metadatos del registro completo
id |
SEDICI_39e09787f78e3d19a085cf8e997d091e |
---|---|
oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/40173 |
network_acronym_str |
SEDICI |
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 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo 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://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 |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/09.pdf 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) |
dc.format.none.fl_str_mv |
application/pdf 171-196 |
dc.source.none.fl_str_mv |
reponame:SEDICI (UNLP) instname:Universidad Nacional de La Plata instacron:UNLP |
reponame_str |
SEDICI (UNLP) |
collection |
SEDICI (UNLP) |
instname_str |
Universidad Nacional de La Plata |
instacron_str |
UNLP |
institution |
UNLP |
repository.name.fl_str_mv |
SEDICI (UNLP) - Universidad Nacional de La Plata |
repository.mail.fl_str_mv |
alira@sedici.unlp.edu.ar |
_version_ |
1844615832214175744 |
score |
13.070432 |