  In this article, we consider the residual regularization path-following
method with the trust-region updating strategy for the linear complementarity
problem. This time-stepping selection based on the trust-region updating
strategy overcomes the shortcoming of the line search method, which consumes
the unnecessary trial steps in the transient-state phase. In order to improve
the robustness of the path-following method, we use the residual regularization
parameter to replace the traditional complementarity regularization parameter.
Moreover, we prove the global convergence of the new method under the standard
assumptions without the traditional assumption 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 cases. 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.
