A new three-term Hestenes-Stiefel type method for nonlinear monotone operator equations and image restoration

In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.