On the Convergence Analysis of a Gradient-Free Projection Method for Nonlinear Equations

Abstract

            This paper aims to obtain a global convergence result for a gradient-free projection method for finding the solution to a nonlinear equation with convex constraints. The direction of the proposed method involves a spectral parameter which generates a sufficient descent direction at each iteration. Furthermore, the global convergence of the proposed method is based on Lipschitz continuity and a weaker monotonicity assumption.