求解张量随机互补问题的光滑牛顿算法

Smoothing Newton method for the tensor stochastic complementarity problem

近年来,越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量,并提出了张量随机互补问题。本文通过引入一类光滑函数,提出了求解张量随机互补问题的一种光滑牛顿算法,并证明了算法的全局和局部收敛性,最后通过数值实验验证了算法的有效性。

In recent years,more and more people realize that stochastic complementarity problem plays an important role in economic management.Some scholars have extended the stochastic complementarity problem from matrices to tensors and proposed the stochastic complementarity problem of tensors.In this paper,we introduce a class of smooth functions,propose a smooth Newton algorithm,and prove the global and local convergence of the algorithm.Finally,the effectiveness of the algorithm is verified by numerical experiments.