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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.