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

Author

Listed:
  • Jie Jiang

    (Chongqing University
    The Hong Kong Polytechnic University)

  • Xiaojun Chen

    (The Hong Kong Polytechnic University)

  • Zhiping Chen

    (Xi’an Jiaotong University)

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.

Suggested Citation

  • Jie Jiang & Xiaojun Chen & Zhiping Chen, 2020. "Quantitative analysis for a class of two-stage stochastic linear variational inequality problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 431-460, June.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:2:d:10.1007_s10589-020-00185-z
    DOI: 10.1007/s10589-020-00185-z
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    References listed on IDEAS

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    1. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    3. Jinlong Lei & Uday V. Shanbhag & Jong-Shi Pang & Suvrajeet Sen, 2020. "On Synchronous, Asynchronous, and Randomized Best-Response Schemes for Stochastic Nash Games," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 157-190, February.
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    Cited by:

    1. Zhen-Ping Yang & Gui-Hua Lin, 2021. "Variance-Based Single-Call Proximal Extragradient Algorithms for Stochastic Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 393-427, August.
    2. Jie Jiang & Shengjie Li, 2021. "Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 650-671, August.
    3. Jie Jiang, 2024. "Distributionally Robust Variational Inequalities: Relaxation, Quantification and Discretization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 227-255, October.
    4. Jie Jiang & Hailin Sun, 2023. "Monotonicity and Complexity of Multistage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 433-460, February.
    5. Bin Zhou & Jie Jiang & Hailin Sun, 2024. "Dynamic stochastic projection method for multistage stochastic variational inequalities," Computational Optimization and Applications, Springer, vol. 89(2), pages 485-516, November.

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