论文标题
线性互补性问题的残留正则通路跟踪方法
Residual regularization path-following methods for linear complementarity problems
论文作者
论文摘要
在本文中，我们将使用线性互补问题的信任区域更新策略考虑剩余正则遵循方法。基于信任区域更新策略的时间步变的选择克服了线路搜索方法的缺点，该方法在瞬态阶段消耗了不必要的试验步骤。为了提高路径遵循方法的鲁棒性，我们使用剩余正则化参数替换传统的互补性正则化参数。此外，我们证明了新方法在标准假设下的全球融合，而没有优先级的传统假设条件与互补性的可行性。数值结果表明，对于线性互补问题，新方法是强大而有效的，尤其是对于密集的情况。它比某些最先进的求解器（例如内置子例程路径和GAMS v28.2（2019）环境的内置子例程路径和数英里）更强大，更快。新方法的计算时间约为密集线性互补问题的路径的1/3至1/10。
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.
