Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions

This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an...

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Autores Principales: Cabuzel, Catherine, Pietrus, Alain, Burnet, Steeve
Formato: Artículo
Idioma: Inglés
Publicado: 2015
Materias:
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/17519
http://hdl.handle.net/10669/13061
id RepoKERWA13061
recordtype dspace
spelling RepoKERWA130612017-08-08T18:50:29Z Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions Convergencia local de los métodos de newton exacto e inexacto para inclusiones variacionales subanalíticas Cabuzel, Catherine Pietrus, Alain Burnet, Steeve función multivaluada inclusión variacional semi-estabilidad hemi-estabilidad función subanalítica método de Newton método de Newton inexacto This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an Inexact Newton type sequence and with some semistability and hemistability properties of the solution x∗ of the previous inclusion, we prove the existence of a sequence which is locally superlinearly convergent. En este artículo se estudia un método iterativo para resolver una inclusión variacional de la forma 0 ∈ f (x) + F (x), donde f es una función punto-conjunto, subanalítica, localmente Lipschitz y F es una función multivaluada de Rn en los subconjuntos cerrados de Rn. A esta inclusión se le asocia, en primer lugar, una sucesión tipo Newton y, posteriormente una sucesion tipo Newton inexacto. Bajo algunas propiedades de semi-estabilidad y hemi-estabilidad de la solución x∗ de la inclusión variacional, se demuestra la existencia de una sucesión que es superlinealmente localmente convergente. 2015-05-19T19:12:57Z 2015-05-19T19:12:57Z 2015-01-01 00:00:00 2015-05-19T19:12:57Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://revistas.ucr.ac.cr/index.php/matematica/article/view/17519 http://hdl.handle.net/10669/13061 10.15517/rmta.v22i1.17519 en Revista de Matemática: Teoría y Aplicaciones Vol. 22 Núm. 1 2015 31-47
institution Universidad de Costa Rica
collection Repositorio KERWA
language Inglés
topic función multivaluada
inclusión variacional
semi-estabilidad
hemi-estabilidad
función subanalítica
método de Newton
método de Newton inexacto
spellingShingle función multivaluada
inclusión variacional
semi-estabilidad
hemi-estabilidad
función subanalítica
método de Newton
método de Newton inexacto
Cabuzel, Catherine
Pietrus, Alain
Burnet, Steeve
Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
description This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an Inexact Newton type sequence and with some semistability and hemistability properties of the solution x∗ of the previous inclusion, we prove the existence of a sequence which is locally superlinearly convergent.
format Artículo
author Cabuzel, Catherine
Pietrus, Alain
Burnet, Steeve
author_sort Cabuzel, Catherine
title Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
title_short Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
title_full Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
title_fullStr Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
title_full_unstemmed Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
title_sort local convergence of exact and inexact newton’s methods for subanalytic variational inclusions
publishDate 2015
url http://revistas.ucr.ac.cr/index.php/matematica/article/view/17519
http://hdl.handle.net/10669/13061
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score 10.575364