Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation
Loading...
Links to Files
Author/Creator
Author/Creator ORCID
Date
2022-11-21
Type of Work
Department
Program
Citation of Original Publication
CHEN, XIAOJUN and JINGLAI SHEN. “Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation,” SIAM J. OPTIM 32 4 (November, 2022): 2909 – 37. https://doi.org/10.1137/21M145536X
Rights
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Subjects
Abstract
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 C¹× γ, where C¹ is the space of continuously differentiable functions and γ is the space of measurable functions, and discuss non-Zeno behavior. We use the sample aver-age 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.