A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices

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.