随机仿射变分不等式的改进期望加权残差法

Improved method of weighted expected residual for solving stochastic variational inequality problems

摘要:

文章在绝对值残差和加权期望残差方法的基础上，针对带有非线性扰动的随机仿射变分不等式问题考虑期望和方差的凸组合形式，得到了改进的期望加权残差极小化问题.通过拟蒙特卡洛方法得到了问题的离散近似问题，研究了问题目标函数的可微性及其水平集的有界性，最后对问题进行了收敛性分析。

Abstract:

This paper is concerned in constructing a new deterministic model for the stochastic affine variational inequality problems with nonlinear perturbation based on the least absolute deviation method and weighted expected residual minimization method. By means of Quasi-Monte Carlo method, we obtain a discrete approximation of the problem. Some properties of the problem are studied under suitable conditions. The convergence of optimal solutions and stationary points of the approximation problem are also analyzed.