Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem

Autores
Carrizo, Gabriel Aníbal; Lotito, Pablo Andres; Maciel, Maria Cristina
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.
Fil: Carrizo, Gabriel Aníbal. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lotito, Pablo Andres. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina
Fil: Maciel, Maria Cristina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Materia
Convergence
Multiobjective Optimization
Newton Method
Trust Region
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:11336/58911
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problemCarrizo, Gabriel AníbalLotito, Pablo AndresMaciel, Maria CristinaConvergenceMultiobjective OptimizationNewton MethodTrust Regionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.Fil: Carrizo, Gabriel Aníbal. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lotito, Pablo Andres. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; ArgentinaFil: Maciel, Maria Cristina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaSpringer2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/58911Carrizo, Gabriel Aníbal; Lotito, Pablo Andres; Maciel, Maria Cristina; Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem; Springer; Mathematical Programming; 159; 1-2; 9-2016; 339-3690025-56101436-4646CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10107-015-0962-6info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10107-015-0962-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:13:22Zoai:ri.conicet.gov.ar:11336/58911instacron: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 10:13:23.113CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
title Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
spellingShingle Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
Carrizo, Gabriel Aníbal
Convergence
Multiobjective Optimization
Newton Method
Trust Region
title_short Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
title_full Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
title_fullStr Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
title_full_unstemmed Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
title_sort Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
dc.creator.none.fl_str_mv Carrizo, Gabriel Aníbal
Lotito, Pablo Andres
Maciel, Maria Cristina
author Carrizo, Gabriel Aníbal
author_facet Carrizo, Gabriel Aníbal
Lotito, Pablo Andres
Maciel, Maria Cristina
author_role author
author2 Lotito, Pablo Andres
Maciel, Maria Cristina
author2_role author
author
dc.subject.none.fl_str_mv Convergence
Multiobjective Optimization
Newton Method
Trust Region
topic Convergence
Multiobjective Optimization
Newton Method
Trust Region
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 trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.
Fil: Carrizo, Gabriel Aníbal. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lotito, Pablo Andres. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina
Fil: Maciel, Maria Cristina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
description A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
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/11336/58911
Carrizo, Gabriel Aníbal; Lotito, Pablo Andres; Maciel, Maria Cristina; Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem; Springer; Mathematical Programming; 159; 1-2; 9-2016; 339-369
0025-5610
1436-4646
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58911
identifier_str_mv Carrizo, Gabriel Aníbal; Lotito, Pablo Andres; Maciel, Maria Cristina; Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem; Springer; Mathematical Programming; 159; 1-2; 9-2016; 339-369
0025-5610
1436-4646
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10107-015-0962-6
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10107-015-0962-6
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 Springer
publisher.none.fl_str_mv Springer
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 13.069144

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