AN IMPROVED LOCAL CONVERGENCE ANALYSIS FOR SECANT-LIKE METHOD
Ioannis Konstantinos Argyros, Saïd Hilout · East Asian Mathematical Journal · 2007
Abstract. We provide a local convergence analysis for Secant–like algorithm for solving nonsmooth variational inclusions in Ba-nach spaces. An existence–convergence theorem and an improve-ment of the ratio of convergence of this algorithm are given undercenter–conditioned divided difference and Aubin’s continuity con-cept. Our result compare favorably with related obtained in [16]. 1. IntroductionThis paper considers the problem of approximating a locally uniquesolution of nondifferentiable generalized equations using an unipara-metric secant–type algorithm. Let X , Y be two Banach spaces, F isa continuous function from X into Y and G is a set–valued map from X to the subsets of Y with closed graph. We consider a generalizedequation in the form(1.1) 0 ∈ F ( x )+ G ( x ) . Generalized equations (1.1) was introduced by Robinson [20], [21].(1.1) is an abstract model including mathematical programming prob-lems, variational inequalities, optimal control, complementarity prob-lems and other fields.For approximating locally the unique solution