ACCELERATION OF CONVERGENCE IN DONTCHEV’S ITERATIVE METHOD FOR SOLVING VARIATIONAL INCLUSIONS
Michel Geoffroy, S. Hilout, A. Pietrus, Communicated V. Drensky · 2003
Abstract. In this paper we investigate the existence of a sequence (xk) satisfying 0 ∈ f(xk)+∇f(xk)(xk+1 −xk)+ 1 2∇2f(xk)(xk+1 −xk) 2 +G(xk+1) and converging to a solution x ∗ of the generalized equation 0 ∈ 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 the set-valued map [f(x∗) + ∇f(x ∗)( · − x ∗ ) + 1 2∇2f(x ∗)( · − x ∗ ) 2 + G(·)] −1 is M-pseudo-Lipschitz around (0, x ∗). 1. Introduction. Throughout this paper X