A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property

We present a new smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ -property. The new method is based on a new smoothing function and a nonmonotone line search which contains a monotone line search as a special case. It is proved that the new method is globally and locally superlinearly/quadratically convergent under mild conditions. Preliminary numerical results are also reported which indicate the proposed method is promising.