A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications

Abstract

In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction generated by the proposed method is close to the one yielded by the memoryless BFGS method, and has the sufficient descent property and the trust region property independent of line search technique. Under some mild conditions, we establish the global convergence of the proposed method. Our numerical experiments show the effectiveness and robustness of the proposed method in comparison with two existing algorithms in the literature. Moreover, we show applicability and encouraging efficiency of the proposed method by extending it to solve sparse signal restoration and image de-blurring problems.