A Predictor-corrector Smoothing Newton Method for Solving the Second-order Cone Complementarity

In this paper we study a predictor-corrector smoothing method which were designed by Engelke S. and Kanzow C. for linear programming, 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 method for solving the SOCCP. This algorithm does not have restrictions regarding its starting point . The globally and locally super linearly convergent under suitable assumptions are shown. Some preliminary computational results are reported and the data result prove that this algorithm is superior to the predictor-corrector smoothing method by Chi Xiaoni, Liu Sanyang.