Abstract

CELIA, Jean-Alexis  and  ALAIN, Pietrus. A variant of Newton's method for generalized equations. Rev.colomb.mat. [online]. 2005, vol.39, n.2, pp.97-112. ISSN 0034-7426.

In this article, we study a variant of Newton's method of the following form 0 ε f(x_k) + hΔf(x_kk)(x_k+1 - x_k) + F(x_k+1) where f is a function whose Frechet derivative is K-lipschitz, F is a set-valued map between two Banach spaces X and Y and h is a constant. We prove that this method is locally convergent to x* a solution of 0 ε f(x) + F(x), if the set-valued map [f(x*) + hΔf(x*)(.- x*) + F(.)]^-1 is Aubin continuous at (0, x*) and we also prove the stability of this method.

Keywords : Set-valued mapping; generalized equation; linear convergence; Aubin continuity.

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