2009, 2009(Special): 250-258. doi: 10.3934/proc.2009.2009.250

A fast iterative scheme for variational inclusions

1. 

Laboratoire Analyse Optimisation Contrôle, Dept. de Mathématiques, Université des Antilles et de la Guyane, B.P. 250, 97157 Pointe à Pitre, Guadeloupe, France

Received  July 2008 Revised  February 2009 Published  September 2009

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.
Citation: Michel H. Geoffroy, Alain Piétrus. A fast iterative scheme for variational inclusions. Conference Publications, 2009, 2009 (Special) : 250-258. doi: 10.3934/proc.2009.2009.250
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