In this paper, we present a smoothing Newton method for solving the monotone weighted complementarity problem (WCP). In each iteration of our method, the iterative direction is achieved by solving a system of linear equations and the iterative step length is achieved by adopting a line search. A feature of the line search criteria used in this paper is that monotone and nonmonotone line search are mixed used. The proposed method is new even when the WCP reduces to the standard complementarity problem. Particularly, the proposed method is proved to possess the global convergence under a weak assumption. The preliminary experimental results show the effectiveness and robustness of the proposed method for solving the concerned WCP.

中文翻译：

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混合线搜索的单调加权互补问题的光滑牛顿法。

在本文中，我们提出了一种平滑牛顿法来解决单调加权互补问题（WCP）。在我们方法的每次迭代中，迭代方向是通过求解线性方程组来实现的，迭代步长是通过采用线搜索来实现的。本文使用的行搜索标准的一个特征是混合使用单调和非单行搜索。即使WCP减少到标准互补性问题，所提出的方法也是新的。特别地，证明了该方法在弱假设下具有全局收敛性。初步的实验结果表明了所提出的方法解决相关WCP的有效性和鲁棒性。