A new nonsmooth equations approach to nonlinear complementarity problems

Based on Fischer's function, a new nonsmooth equations approach is presented for solving 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 a 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.