Derivative-free method based on DFP updating formula for solving convex constrained nonlinear monotone equations and application

In this paper, a new derivative-free approach for solving nonlinear monotone system of equations with convex constraints is proposed. The search direction of the proposed algorithm is derived based on the modified scaled Davidon-Fletcher-Powell (DFP) updating formula in such a way that it is sufficiently descent. Under some mild assumptions, the search direction is shown to be bounded. Subsequently, the convergence result of the proposed method is established. The performance of the proposed algorithm on a collection of some test problems as well as signal recovery problems is demonstrated in comparison with some existing algorithms with similar characteristics. The results of the numerical experiments confirm the efficiency as well as the robustness of the proposed algorithm by comparing it with some existing methods in the literature.