A three-term Polak-Ribière-Polyak derivative-free method and its application to image restoration

In this paper, a derivative-free method for solving convex constrained nonlinear equations involving a monotone operator with a Lipschitz condition imposed on the underlying operator is introduced and studied. The proposed method incorporates the projection technique of Solodov and Svaiter with the three-term Polak-Ribière-Polyak conjugate gradient method for the unconstrained optimization problem proposed by Min Li [J. Ind. Manag. Optim.16.1(2020): 245.16.1 (2020): 245]. Under some standard assumptions, we establish the global convergence of the proposed method. Furthermore, we provide some numerical examples and application to image deblurring problem to illustrate the effectiveness and competitiveness of the proposed method. The numerical results indicate that the proposed method is remarkably promising.