In this article, we consider the regularization path-following method with the trust-region updating strategy for the linear complementarity problem. Moreover, we prove the global convergence of the new method under the standard assumptions without the condition of the priority to feasibility over complementarity. Numerical results show that the new method is robust and efficient for the linear complementarity problem, especially for the dense linear complementarity problem. And it is more robust and faster than some state-of-the-art solvers such as the built-in subroutines PATH and MILES of the GAMS v28.2 (2019) environment. The computational time of the new method is about 1/3 to 1/10 of that of PATH for the dense linear complementarity problem.

翻译：在本条中,我们考虑正规化的路径跟踪方法与信任区域线性互补问题更新战略;此外,我们证明,在标准假设下,新方法在标准假设下的全球趋同并不以可行性优于互补性为条件;数字结果显示,新方法对于线性互补问题,特别是对于密集线性互补问题,是稳健和有效的;比一些最先进的解决方案,如GAMS v28.2 (2019年)环境的内置子例PATH和MILES更强大和更快;新方法的计算时间大约是PATH对密集线性互补问题的计算时间为三分之一至1/10。