A new one-step smoothing Newton method for nonlinear complementarity problem with -function

In this paper, nonlinear complementarity problem with P"0-function is studied. Based on a new smoothing function, the problem is approximated by a family of parameterized smooth equations and we present a new one-step smoothing Newton method to solve it. At each iteration, the proposed method only need to solve one system of linear equations and perform one Armijo-type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the solution. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm.