Sub-quadratic convergence of a smoothing Newton method for symmetric cone complementarity problems

In this paper, A smoothing Newton method is proposed to solve the symmetric cone complementarity problems (SCCP). Firstly, we reformulate SCCP as a nonsmooth nonlinear system of equations by the min complementarity function. Secondly, we smooth the nonsmooth equations by the Chen-Harker-Kanzow-Smale (CHKS) smoothing function. At last, Newtons method is applied to the system. The presented method solves only one linear system of equations and performs only one line search at each iteration. Under a nonsingularity assumption the method is globally and locally subquadratically convergent.