Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations

Abstract

In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method.