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A fast iterative scheme for variational inclusions

Pages: 250 - 258, Issue Special, September 2009

 Abstract        Full Text (147.9K)              

Michel H. Geoffroy - Laboratoire Analyse Optimisation Contrôle, Dept. de Mathématiques, Université des Antilles et de la Guyane, B.P. 250, 97157 Pointe à Pitre, Guadeloupe, France (email)
Alain Piétrus - Laboratoire Analyse Optimisation Contrôle, Dept. de Mathématiques, Université des Antilles et de la Guyane, B.P. 250, 97157 Pointe à Pitre, Guadeloupe, France (email)

Abstract: We present an iterative scheme for solving inclusions of the form $f(x) + F(x) \ni 0$ where $f$ is a Lipschitz continuous function admitting a first order divided difference while $F$ stands for a set-valued mapping, both of them acting between Banach spaces. We prove the convergence of our method under several regularity properties for $F$ and without any differentiability assumption on $f$. We investigate, subsequently, the case when the mapping $F$ is metrically regular, strongly metrically regular and strongly metrically subregular.

Keywords:  Set-valued mappings, Metric regularity, Divided differences
Mathematics Subject Classification:  Primary: 49J53, 49J40; Secondary: 90C48

Received: July 2008;      Revised: February 2009;      Published: September 2009.