A One-Step Smoothing Newton Method Based on a New Class of One-Parametric Nonlinear Complementarity Functions for P_0-NCP

摘要

Nonlinear complementarity problem with Po-function is studied. Based on a new class of one-parametric nonlinear complementarity functions, the problem is approximated by a family of parameterized smooth equations and a one-step smoothing Newton method is presented. The proposed algorithm only need to solve one system of linear equations and perform one line search per iteration. It is proved to be convergent globally and super linearly without strict complementarity. Moreover, the algorithm has locally quadratic convergence under mild conditions.