A smoothing Broyden-like method with a nonmonotone derivative-free line search for nonlinear complementarity problems

Abstract

By using the CHKS-function, we propose a smoothing Broyden-like method for general nonlinear complementarity problems (NCPs). The method is based on the smoothing equation for which we consider the smoothing parameter as an independent variable, and makes use of a new nonmonotone derivative-free line search rule. Under suitable assumptions, we show that the iteration sequence generated by the proposed algorithm converges globally and superlinearly. Furthermore, the algorithm has local quadratic convergence under mild assumptions. Some numerical results are reported, which show that the algorithm is quite effective.