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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58911
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T10:00:50Zoai: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:34982025-09-03 10:00:51.052CONICET 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/ |
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openAccess |
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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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.13397 |