A fixed-point method for a class of super-large scale nonlinear complementarity problems

We consider a class of complementarity problems involving functions which are nonlinear. In this paper we reformulate this nonlinear complementarity problem as a system of absolute value equations (which is nonsmooth). Then we propose a fixed-point method to solve this nonsmooth system. We prove that the proposed method is globally linearly convergent under a mild condition. The proposed method is greatly effective not only for small and medium size problems, but also for large and super-large scale problems. Especially, our method can efficiently solve super-large scale problems, with a million variables, in a few tens of minutes on a PC.