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.

中文翻译：

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直角坐标的$$ P_0 $$ P0-性质的对称锥互补问题的一种新的非单调平滑牛顿方法

对于具有笛卡尔\（P_0 \） -性质的对称锥互补问题，我们提出了一种新的平滑牛顿方法。新方法基于新的平滑功能和非单调线搜索，该搜索包含特殊情况下的单调线搜索。证明了该新方法在温和条件下是全局和局部超线性/二次收敛的。初步的数值结果也被报道，表明该方法是有前途的。