Superlinear/quadratic one-step smoothing Newton method for P<Subscript>0</Subscript>-NCP without strict complementarity

We propose a modified one-step smoothing Newton method for solving nonlinear complementarity problems with P <Subscript>0</Subscript>-function (P <Subscript>0</Subscript>-NCP) based on CHKS smoothing function. Our smoothing Newton method solves only one linear system of equations and performs only one line search at each iteration. It is proved that our proposed algorithm has superlinear convergence in absence of strict complementarity assumption at the P <Subscript>0</Subscript>-NCP solution. Under suitable conditions, the modified algorithm has global linear and local quadratic convergence. Compared to previous literatures, our algorithm has stronger convergence results under weaker conditions. Copyright Springer-Verlag Berlin Heidelberg 2002