Motivated by the modulus-based Newton method for solving linear complementarity problems (Zheng and Li, J. Comput. Appl. Math. 288, 116–126 2015; Wu and Li, Calcolo 54, 43–56 2017), we propose a generalized modulus-based Newton method to solve a class of non-linear complementarity problems with P-matrices. A sufficient condition to guarantee the convergence of the proposed method is obtained. Numerical experiments further demonstrate that the proposed method is efficient and has better performance than the existing modulus-based iteration method and the Newton method.

中文翻译：

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求解一类具有P矩阵的非线性互补问题的基于广义模数的牛顿法

受基于模数的牛顿法求解线性互补问题的启发（Zheng and Li, J. Comput. Appl. Math. 288 , 116–126 2015; Wu and Li, Calcolo 54 , 43–56 2017），我们提出了一个广义的基于模数的牛顿法解决一类具有 P 矩阵的非线性互补问题。得到了保证所提方法收敛的充分条件。数值实验进一步表明，所提出的方法是有效的，并且比现有的基于模数的迭代方法和牛顿法具有更好的性能。