Inexact Restoration method for nonlinear optimization without derivatives

Autores
Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in two phases. In the first one, the violation of the feasibility is reduced. In the second one, the objective function is minimized onto a linearization of the nonlinear constraints. At both phases, polynomial interpolation models are used in order to approximate the objective function and the constraints. At the first phase a derivative-free solver for box constrained optimization can be used. For the second phase, we propose a new method ad-hoc based on trust-region strategy that uses the projection of the simplex gradient on the tangent space. Under suitable assumptions, the algorithm is well defined and convergence results are proved. A numerical implementation is described and numerical experiments are presented to validate the theoretical results.
Fil: Arouxet, Maria Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; 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
Materia
Derivative-Free Optimization
Inexact Restoration
Polynomial Interpolation
Trust-Region Methods
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:11336/77601
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Inexact Restoration method for nonlinear optimization without derivativesArouxet, Maria BelenEchebest, Nélida EsterPilotta, Elvio AngelDerivative-Free OptimizationInexact RestorationPolynomial InterpolationTrust-Region Methodshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in two phases. In the first one, the violation of the feasibility is reduced. In the second one, the objective function is minimized onto a linearization of the nonlinear constraints. At both phases, polynomial interpolation models are used in order to approximate the objective function and the constraints. At the first phase a derivative-free solver for box constrained optimization can be used. For the second phase, we propose a new method ad-hoc based on trust-region strategy that uses the projection of the simplex gradient on the tangent space. Under suitable assumptions, the algorithm is well defined and convergence results are proved. A numerical implementation is described and numerical experiments are presented to validate the theoretical results.Fil: Arouxet, Maria Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; 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; ArgentinaElsevier Science2015-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/77601Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Inexact Restoration method for nonlinear optimization without derivatives; Elsevier Science; Journal Of Computational And Applied Mathematics; 290; 5-2015; 26-430377-0427CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2015.04.047info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0377042715002733info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:51:52Zoai:ri.conicet.gov.ar:11336/77601instacron: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:34982025-10-15 14:51:52.868CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Inexact Restoration method for nonlinear optimization without derivatives
title Inexact Restoration method for nonlinear optimization without derivatives
spellingShingle Inexact Restoration method for nonlinear optimization without derivatives
Arouxet, Maria Belen
Derivative-Free Optimization
Inexact Restoration
Polynomial Interpolation
Trust-Region Methods
title_short Inexact Restoration method for nonlinear optimization without derivatives
title_full Inexact Restoration method for nonlinear optimization without derivatives
title_fullStr Inexact Restoration method for nonlinear optimization without derivatives
title_full_unstemmed Inexact Restoration method for nonlinear optimization without derivatives
title_sort Inexact Restoration method for nonlinear 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
Inexact Restoration
Polynomial Interpolation
Trust-Region Methods
topic Derivative-Free Optimization
Inexact Restoration
Polynomial Interpolation
Trust-Region Methods
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in two phases. In the first one, the violation of the feasibility is reduced. In the second one, the objective function is minimized onto a linearization of the nonlinear constraints. At both phases, polynomial interpolation models are used in order to approximate the objective function and the constraints. At the first phase a derivative-free solver for box constrained optimization can be used. For the second phase, we propose a new method ad-hoc based on trust-region strategy that uses the projection of the simplex gradient on the tangent space. Under suitable assumptions, the algorithm is well defined and convergence results are proved. A numerical implementation is described and numerical experiments are presented to validate the theoretical results.
Fil: Arouxet, Maria Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; 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
description A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in two phases. In the first one, the violation of the feasibility is reduced. In the second one, the objective function is minimized onto a linearization of the nonlinear constraints. At both phases, polynomial interpolation models are used in order to approximate the objective function and the constraints. At the first phase a derivative-free solver for box constrained optimization can be used. For the second phase, we propose a new method ad-hoc based on trust-region strategy that uses the projection of the simplex gradient on the tangent space. Under suitable assumptions, the algorithm is well defined and convergence results are proved. A numerical implementation is described and numerical experiments are presented to validate the theoretical results.
publishDate 2015
dc.date.none.fl_str_mv 2015-05
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/11336/77601
Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Inexact Restoration method for nonlinear optimization without derivatives; Elsevier Science; Journal Of Computational And Applied Mathematics; 290; 5-2015; 26-43
0377-0427
CONICET Digital
CONICET
url http://hdl.handle.net/11336/77601
identifier_str_mv Arouxet, Maria Belen; Echebest, Nélida Ester; Pilotta, Elvio Angel; Inexact Restoration method for nonlinear optimization without derivatives; Elsevier Science; Journal Of Computational And Applied Mathematics; 290; 5-2015; 26-43
0377-0427
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2015.04.047
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0377042715002733
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 Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.22299

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