Prépublication AOC numéro 02-04
Acceleration of Convergence in Dontchev's Iterative Method for Solving Variational Inclusions
GEOFFROY, Michel - Laboratoire A.O.C.,
Université des Antilles et de la
Guyane, Pointe-à-Pitre, F-97157 cedex
HILOUT, Saïd -
Département de Mathématiques Appliquées,
Faculté des Sciences et Techniques,
BP 523, Beni-Mellal, Maroc
PIETRUS, Alain -
Laboratoire A.O.C., Université des Antilles et
de la Guyane, Pointe-à-Pitre, F-97157 cedex
Mots Clés :
Multiapplications, Aubin Continuity, Cubic Convergence.
Classification MSC : 47H04; 65K10
Abstract : -
We investigate the existence of some sequence
(xk) satisfying 0 Î
f(xk)+ Ñf(xk)
(xk+1-xk) + 1/2 Ñ
2 f(xk)
(xk+1-xk)2 +G(xk+1) and converging to
a solution x* of the generalized equation
0 Î f(x)+G(x); where
f is a function and G is a set-valued map acting in Banach spaces. We
show that the previous sequence is locally cubic convergent to x*
whenever some set-valued map involving G, f and its first and second
Fréchet derivatives is M-pseudo-Lipschitz around (0,x*).
Article :
Postscript compressé
Contact :
michel.geoffroy@univ-ag.fr