One-step smoothing inexact Newton method for nonlinear complementarity problem with a $P_0$ function

Abstract

Based on Fischer-Burmeister function, we propose a new smoothing function. Using this function,the existence and continuity of the smooth path for solving the nonlinear complementarity problem with a $P_0$ function are discussed. Then we present a one-step smoothing inexact Newton method for nonlinear complementarity problem with a $P_0$ function. The proposed method solves the corresponding linear system approximately in each iteration. Furthermore, we investigate the boundedness of the sequence generated by our algorithm and prove the global convergence and local superlinear convergence under mild conditions.