A new nonsmooth equations approach to nonlinear complementarity problems

Based on Fischer's function, a new nonsmooth equations approach is presented for serving nonlinear complementarity problems. Under some suitable assumptions, a local and Q-quadratic convergence result is established for the generalized Newton method applied to the system of nonsmooth equations, which is it reformulation of nonlinear complementarity problems. To globalize the generalized Newton method, a hybrid method combining the generalized Newton method with the steepest descent method is proposed. Global and Q-quadratic convergence is established for this hybrid method. Some numerical results are also reported.