Full paper in PDF format:
$%C. Cabuzel and A. Piétrus, Solving variational iby a method obtained using a multipoint iteration formula, Rev. Mat. Complut. 22 (2009), no. 1, 63–74.%$

Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula

Catherine CABUZEL and Alain PIÉTRUS

Laboratoire Analyse, Optimisation, Contrôle
Université des Antilles et de la Guyane
Département de Mathématiques et Informatique
Campus de Fouillole
F-97159 Pointe-à-Pitre — France
catherine.zebre@univ-ag.fr apietrus@univ-ag.fr

Received: March 26, 2007
Accepted: February 18, 2008

ABSTRACT

This paper deals with variational inclusions of the form: $0 ∈f(x)+ F(x)$ where $f$ is a single function admitting a second order Fréchet derivative and $F$ is a set-valued map acting in Banach spaces. We prove the existence of a sequence $(xk)$ satisfying $0∈ f(x )+∑M a ∇f(x + β(x - x ))(x - x )+ F(x ) k i=1 i k i k+1 k k+1 k k+1$ where the single-valued function involved in this relation is an approximation of the function $f$ based on a multipoint iteration formula and we show that this method is locally cubically convergent.

Key words: set-valued mapping, generalized equations, pseudo-Lipschitz maps, multipoint iteration formula.
2000 Mathematics Subject Classification: 49J53, 47H04, 65K10.