Quantitative stability of the ERM formulation for a class of stochastic linear variational inequalities

Jianxun Liu; Shengjie Li; Yingrang Xu

doi:10.3934/jimo.2021083

Article Contents

2022, Volume 18, Issue 4: 2599-2610. Doi: 10.3934/jimo.2021083

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Quantitative stability of the ERM formulation for a class of stochastic linear variational inequalities

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

^* Corresponding author: Shengjie Li
^* Corresponding author: Shengjie Li

Received: October 31, 2020

Revised: February 28, 2021

Published: July 2022

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Abstract

This paper focuses on the quantitative stability analysis of the expected residual minimization (ERM) formulation for a class of stochastic linear variational inequalities. Firstly, the existence of solutions of the ERM formulation and its perturbed problem is discussed. Then, the quantitative stability of the ERM formulation is derived under suitable probability metrics. Finally, the sample average approximation (SAA) problem of the ERM formulation is studied, and the rates of convergence of optimal solution sets are obtained under different assumptions.

Keywords:

Stochastic variational inequality problem,
ERM formulation,
quantitative stability analysis,
sample average approximation,
rate of convergence.

Mathematics Subject Classification: 90C15, 90C33.

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