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

Jie Jiang (), Xiaojun Chen () and Zhiping Chen ()
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Jie Jiang: Chongqing University
Xiaojun Chen: The Hong Kong Polytechnic University
Zhiping Chen: Xi’an Jiaotong University

Computational Optimization and Applications, 2020, vol. 76, issue 2, No 5, 460 pages

Abstract: 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.

Keywords: Two-stage stochastic variational inequality; Quantitative stability; Discrete approximation; Exponential convergence; Non-cooperative game (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10589-020-00185-z

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