A derivative-free conjugate gradient method for large-scale nonlinear systems of monotone equations

This paper presents a derivative-free conjugate gradient type algorithm for large-scale nonlinear systems of monotone equations. New search directions with superior numerical performance are constructed by introducing a new conjugate parameter and particular spectral parameters. These search directions inherit the numerical stability of RMIL search direction and satisfy the sufficient descent condition independent of step size. The method combines the hyperplane projection and the derivative-free line search technique to compute the iteration points. Under some appropriate assumptions, the global convergence of the given methods is established. Numerical experiments indicate that the proposed algorithms are effective.