An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications

Abstract

This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first generates a specific direction and then employs a line search strategy along the direction to calculate a new iterate. If the new iterate solves the problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set (constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent condition and the global convergence of the method is established under suitable assumptions. Finally, some numerical experiments were presented to show the performance of the proposed method in solving nonlinear equations and its application in image recovery problems.