The Research Of Smoothing Methods For The Second-order Cone Programming And Its Complementarity Problem

In this paper, we study the smoothing methods for second-order cone programming (SOCP) and second-order cone complementarity problem(SOCCP). In order to improving convergence rate, a new smoothing function for the second-order cone programming is given by smoothing the symmetric perturbed CHKS function. Based on this new function, a smoothing Newton method is presented for solving the second-order cone programming. The proposed algorithm solves only one system of equations which is equivalent to the optimization conditions. This algorithm does not have restrictions regarding its starting point and it has quadratic convergence rate.Based on the new function, SOCP is equivalent to solving nonlinear equations which is extended to SOCCP, so that it is not only equivalent to a smooth complementary function, but transformed into equivalent nonlinear equations, with the assumption that F is P0 function andΦ( z) is coercive function, we prove that the sequence generated by the algorithm remains in some level set and it has a quadratic convergence rate. Numerical results suggest the effectiveness of our algorithm.