The convergence of a one-step smoothing Newton method for P0P0-NCP based on a new smoothing NCP-function

The nonlinear complementarity problem (denoted by NCP(F  )) can be reformulated as the solution of a nonsmooth system of equations. By introducing a new smoothing NCP-function, the problem is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is proposed for solving the nonlinear complementarity problem with P0P0-function (P0P0-NCP) based on the new smoothing NCP-function. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. Without requiring strict complementarity assumption at the P0P0-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions.