论文标题
通过直接型方法解决非主体平衡问题
Solving non-monotone equilibrium problems via a DIRECT-type approach
论文作者
论文摘要
提出了一种用于解决非主持酮平衡问题（EPS）的全球优化方法。 （正则）差距函数类用于将任何EP作为一个受约束的全局优化程序重新重新调整，并提供了Lipschitz常数的某些界限。提出的全局优化方法是\ texttt {direct}算法的改进版本的组合，该算法利用了目标函数的Lipschitz常数的局部界限，以及本地最小化。与大多数现有的EPS解决方案方法不同，本文没有假定单调性型条件。几类EPS的初步数值结果显示了该方法的有效性。
A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the \texttt{DIRECT} algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.
