Regularization path-following methods with the trust-region updating strategy for linear complementarity problems

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.