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

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  • 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.
    Mathematics Subject Classification: Primary: 65H10, 65K05 Secondary: 90C26.

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