Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications

Abstract

This article proposes an optimal value for the scaled Perry conjugate gradient (CG) method, which aims to solve large-scale monotone nonlinear equations. An optimal choice for the scaled parameter is obtained by minimizing the largest and smallest eigenvalues of the search direction matrix. In addition, the corresponding Perry CG parameter is incorporated with the hyperplane approach to propose a robust algorithm for solving monotone equations. The global convergence of the proposed method is established based on monotonicity and Lipschitz continuity assumptions. The robustness of the proposed algorithm is validated by examples involving numerical solving of monotone equations with their application to signal and image restoration problems.