求解一类特殊随机广义垂直线性互补问题的光滑化SAA方法

A smoothing SAA method for a special case of stochastic generalized vertical linear complementary problem

随机广义垂直线性互补问题(SEVLCP)是一类随机均衡问题,在金融工程、管理科学、交通均衡、博弈论等领域有重要的应用.基于CHKS函数,提出了一类特殊广义垂直线性互补问题的光滑化函数,并在此基础上研究了一类特殊随机广义垂直互补问题的光滑化样本均值近似方法.在一定的条件下给出了样本充分大时保证光滑化样本均值近似问题解的存在性的充分性条件并建立了这类方法的收敛性分析,即当样本数目充分大时,光滑化样本均值近似问题的最优解接近随机广义垂直互补问题的解.

The stochastic generalized vertical linear complementary problem is a kind of stochastic equilibrium problem,which plays an important role in some areas for instance,financial engineering、management science transportation equilibrium and games theory.In this paper,based on the CHKS function,a smoothing function for a special case of generalized vertical linear complementary problem is proposed and then a smoothing sample average approximation method for solving this kind of stochastic generalized vertical complementary problem based on the CHKS function is studied.Under certain conditions,the sufficient conditions ensuring existence of solution of smoothed sample average approximation problem are obtained when the sample size is large enough and the convergence analysis of this method is established,that is,the optimal solution of smoothed sample average approximation problem approximates the solution of stochastic generalized vertical complementary problem when the sample size is large enough.