A derivative-free method for solving large-scale nonlinear systems of equations

In this paper, a fully derivative-free method for solving large-scale nonlinear systems of equations is presented. It uses in a systematic way the well-known Polak-Ribière-Polyak (PRP) conjugate gradient direction as a search direction and employs a backtracking process to obtain a suitable stepsize. Assume that the nonlinear mapping is Lipschitz continuous, some global convergence results are established. A modification of this method which may allow the objective function's sufficiently nonmonotone behavior is also presented in this paper. Numerical comparisons using a set of large-scale test problems in the CUTE library show that the proposed methods are encouraging.