Predictor-Corrector Smoothing Newton Method for Solving the Second-order cone Complementarity

摘要

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.