A smoothing Newton method based on a one-parametric class of smoothing function for SOCCP

摘要

In this paper, the monotone second order cone complementarity problem (SOCCP) is studied. Based on a new class of one-parametric τ∈[0,4) smoothing functions, a smoothing Newton method was proposed for this problem. The proposed method solves only one linear system of equations and one line search at each iteration, and has no restrictions on its starting point. Moreover, the global and Q-quadratically local convergence of the algorithm are obtained without strict complementarity. We also give a numerical example about 2×2 P ₀-matrix, which implies that the smoothing Newton method based on CHKS smoothing function (when τ=0) can not be used for solving the class of nonmonotone P ₀-SOCCP. At last, the preliminary numerical results are also reported.