Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation
Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation
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DOI：
10.1137/21m145536x
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发表时间：
2022-11
期刊：
影响因子：
--
通讯作者：
Xiaojun Chen;Jinglai Shen
中科院分区：
文献类型：
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作者：
Xiaojun Chen;Jinglai Shen
． 为了解决动态变分不等式中的不确定性问题，研究了动态随机变分不等式。在c1 ×Y中，当c1为连续可微函数空间，Y为可测函数空间时，我们证明了一类dsv解的存在唯一性，并讨论了非zeno行为。我们使用样本平均近似（SAA）和时间步进格式作为离散近似来处理dsvi的不确定性和动力学。在此基础上，我们证明了DSVI的SAA的一致收敛性和指数收敛率。提出了一种时间步进迭代子空间能量直接反演（EDIIS）方法来求解DSVI的SAA引起的DVI；证明了其收敛性。我们的结果用交通分配问题中瞬时动态用户均衡的点队列模型来说明。
. This paper studies dynamic stochastic variational inequalities (DSVIs) to deal with uncertainties in dynamic variational inequalities (DVIs). We show the existence and uniqueness of a solution for a class of DSVIs in C 1 ×Y , where C 1 is the space of continuously differentiable functions and Y is the space of measurable functions, and discuss non-Zeno behavior. We use the sample average approximation (SAA) and time-stepping schemes as discrete approximation for the uncertainty and dynamics of the DSVIs. We then show the uniform convergence and an exponential convergence rate of the SAA of the DSVI. A time-stepping EDIIS (energy direct inversion on the iterative subspace) method is proposed to solve the DVI arising from the SAA of DSVI; its convergence is established. Our results are illustrated by a point-queue model for an instantaneous dynamic user equilibrium in traffic assignment problems.