Predictor-corrector smoothing Newton method, based on a new smoothing function, for solving the nonlinear complementarity problem with a P0 function

By smoothing a perturbed minimum function, we propose in this paper a new smoothing function. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P-0 function are discussed. We investigate the boundedness of the iteration sequence generated by noninterior continuation/ smoothing methods under the assumption that the solution set of the NCP is nonempty and bounded. Based on the new smoothing function, we present a predictor-corrector smoothing Newton algorithm for solving the NCP with a P-0 function, which is shown to be globally linearly and locally superlinearly convergent under suitable assumptions. Some preliminary computational results are reported.