Predictor-Corrector Smoothing Newton Method for Solving the Second-Order Cone Complementarity

In this paper we study predictor-corrector smoothing Newton method which were designed by Z. H. Huang, J. Han, and Z. Chen for nonlinear complementarity problem, we extends the Algorithm to second-order cone complementarity (SOCCP). Based on the Chen and Mangasarian smoothing function, we present a predictor-corrector smoothing Newton algorithm for solving the SOCCP. The neighbourhood of the path does not appear in the Algorithm. Thus, it does not need a few additional computations which keep the iteration sequence staying in the given neighbourhood. The algorithm is simpler than a predictor-corrector smoothing method by Chi Xiaoni, Liu Sanyang and this algorithm does not have restrictions regarding its starting point. The globally and locally superlinearly convergent under suitable assumptions are shown. Some preliminary computational results are reported.