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On the convergence of some methods for variational inclusions

  • C. Jean-Alexis
  • A. Piétrus
Article

Abstract

In this paper, we study variational inclusions of the following form 0 ∈f(x) + g(x) + F(x) (*) wheref is differentiable in a neighborhood of a solutionx* of (*) andg is differentiable atx* and F is a set-valued mapping with closed graph acting in Banach spaces. The method introduced to solve (*) is superlinear and quadratic when ∇f is Lipschitz continuous.

Keywords

Set-valued mappings variational inclusions superlinear convergence pseudo-Lipschitz mappings divided difference 

Mathematics Subject Classifications

49J53 47H04 65K10 

Sobre la convergencia de algunos métodos para inclusiones variacionales

Resumen

En este artículo se estudian inclusiones variacionales de la forma 0 ∈f(x) + g(x) + F(x) (*) dondef es diferenciable en un entorno de la soluciónx* de (*),g es diferenciable enx* yF es una aplicación con gráfica cerrada entre espacios de Banach. El método introducido para resolver (*) es superlineal y cuadrático cuando ∇f es continuo y verifica la condición de Lipschtz.

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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Laboratoire Analyse, Optimisation, ContrôleUniversité des Antilles et de la Guyane Département de Mathématiques et InformatiquePointe-à-PitreFrance

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