A derivative-free nonmonotone line search and its application to the spectral residual method

In this paper we propose a derivative-free nonmonotone line search for solving large-scale nonlinear systems of equations. Under appropriate conditions, we show that the spectral residual method with this line search is globally convergent. We also present some numerical experiments. The results show that the spectral residual method with the new nonmonotone line search is promising.