Quantitative analysis for a class of two‑stage stochastic linear variational inequality problems

Jie Jiang, Xiaojun Chen, Zhiping Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

This paper considers a class of two-stage stochastic linear variational inequality
problems whose first stage problems are stochastic linear box-constrained variational inequality problems and second stage problems are stochastic linear complementary problems having a unique solution. We first give conditions for the existence of solutions to both the original problem and its perturbed problems. Next we derive quantitative stability assertions of this two-stage stochastic problem under total variation metrics via the corresponding residual function. Moreover, we study the discrete approximation problem. The convergence and the exponential rate of convergence of optimal solution sets are obtained under moderate assumptions respectively. Finally, through solving a non-cooperative game in which each player’s problem is a parameterized two-stage stochastic program, we numerically illustrate our theoretical results.
Original languageEnglish
Pages (from-to)431-460
Number of pages30
JournalComputational Optimization and Applications
Volume76
Issue number2
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Discrete approximation
  • Exponential convergence
  • Non-cooperative game
  • Quantitative stability
  • Two-stage stochastic variational inequality

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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