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On the convergence of some methods for variational inclusions

Sobre la convergencia de algunos métodos para inclusiones variacionales

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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.

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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Correspondence to C. Jean-Alexis.

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Jean-Alexis, C., Piétrus, A. On the convergence of some methods for variational inclusions. Rev. R. Acad. Cien. Serie A. Mat. 102, 355–361 (2008). https://doi.org/10.1007/BF03191828

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Keywords

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

Mathematics Subject Classifications

  • 49J53
  • 47H04
  • 65K10