A New Hybrid Spectral Gradient Projection Method for Monotone System of Nonlinear Equations with Convex Constraints

Abstract

Spectral gradient methods and projection technique have motivated many numerical methods for solving monotone equations. In this work, we proposed a hybrid spectral gradient algorithm for system of nonlinear monotone equations with convex constraints. The method is a combination of a convex combination of two different positive spectral parameters and the projection technique. The global convergence of the method was established under the assumptions of monotonicity and Lipschitz continuity.  Numerical results presented by means of comparative experiments with a similar method shows the proposed method is very efficient.