Analysis of a smoothing Newton method for second-order cone complementarity problem

Abstract

In this paper, we consider the second-order cone complementarity problem with P0-property. By introducing a smoothing parameter into the Fischer-Burmeister function, we present a smoothing Newton method for the second-order cone complementarity problem. The proposed algorithm solves only a linear system of equations and performs only one line search at each iteration. At the same time, the algorithm does not have restrictions on its starting point and has global convergence. Under the assumption of nonsingularity, we establish the locally quadratic convergence of the algorithm without strict complementarity condition. Preliminary numerical results show that the algorithm is promising.