Prépublication AOC numéro 03-07
Local Convergence of Some Iterative Methods
for Generalized Equations
GEOFFROY, Michel H. - Laboratoire A.O.C.,
Université des Antilles et de la
Guyane, Pointe-à-Pitre, F-97159 cedex
PIETRUS, Alain -
Laboratoire A.O.C., Université des Antilles et
de la Guyane, Pointe-à-Pitre, F-97159 cedex
Mots Clés :
Generalized equations, set-valued maps, Aubin continuity, super-linear convergence,
quadratic convergence.
Classification MSC : 47H04; 65K10.
Abstract : -
We are interested in studying generalized equations of the following form:
0 Î f(x)+g(x)+F(x) (*); where
f and g are functions such that g is not necessarily differentiable except
at the solution of (*) and where F is a set-valued
map acting in Banach spaces. We prove the existence of
a sequence (xk) satisfying
0 Î
f(xk)+ g(xk)+ ( Ñf(xk)
[xk-1,xk;g])(xk+1-xk)
+F(xk+1) and which is super-linearly convergent to a solution
of (*). Afterwards, we provide two variants of our major result involving
super-linear and quadratic convergent sequences.
Article :
Postscript compressé
Contact :
michel.geoffroy@univ-ag.fr