A New Smoothing Newton Method for Symmetric Cone Complementarity Problems

Based on a new smoothing function, a smoothing Newton-type method is proposed for the solution of symmetric cone complementarity problems (SCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. Moreover, it does neither have restrictions on its starting point nor need additional computation which keep the iteration sequence staying in the given neighborhood. Finally, the global and Q-quadratical convergence is shown. Numerical results suggest that the method is effective.