Local convergence of some iterative methods for generalized equations

摘要

We study generalized equations of the following form: 0 epsilon f(x) + g(x) + F(x), where f is Frdchet differentiable in a neighborhood of a solution x* of (*) and g is Frechet differentiable at x* and where F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (x(k)) satisfying 0 epsilon f(x(k)) + 9(x(k)) + (delf (x(k)) + [x(k-1), x(k); g]) (x(k+1) - x(k)) + F(x(k+1)) which is super-linearly convergent to a solution of (*). We also present other versions of this iterative procedure that have superlinear and quadratic convergence, respectively. (C) 2003 Elsevier Inc. All rights reserved. [References: 17]