Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation
| dc.contributor.author | CHEN, XIAOJUN | |
| dc.contributor.author | SHEN, JINGLAI | |
| dc.date.accessioned | 2022-12-22T18:56:18Z | |
| dc.date.available | 2022-12-22T18:56:18Z | |
| dc.date.issued | 2022-11-21 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | The first author’s work was supported in part by the Hong Kong Research GrantsCouncil, grant PolyU15300120. The second author’s work was partially supported by NSF grantCMMI-1902006. | en_US |
| dc.description.uri | https://epubs.siam.org/doi/abs/10.1137/21M145536X | en_US |
| dc.format.extent | 29 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.identifier | doi:10.13016/m2wi9s-drk0 | |
| dc.identifier.citation | 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 | en_US |
| dc.identifier.uri | https://doi.org/10.1137/21M145536X | |
| dc.identifier.uri | http://hdl.handle.net/11603/26503 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | SIAM | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.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. | en_US |
| dc.title | Dynamic Stochastic Variational Inequalities and Convergence of Discrete Approximation | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0003-2172-4182 | en_US |