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Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities

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  • Jie Jiang

    (Chongqing University)

  • Shengjie Li

    (Chongqing University)

Abstract

Sample average approximation (SAA) approach for two-stage stochastic variational inequalities (SVIs) with continuous probability distributions, where the second-stage problems have multiple solutions, may not promise convergence assertions as the sample size tends to infinity. In this paper, a regularized SAA approach is proposed to numerically solve a class of two-stage SVIs with continuous probability distributions, where the second-stage problems are monotone and allowed to have multiple solutions. We first give some structural properties. After that, the convergence analysis of the regularized SAA approach for two-stage SVIs is investigated as the regularization parameter tends to zero and the sample size tends to infinity. Finally, we employ the progressive hedging algorithm to report some numerical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:2:d:10.1007_s10957-021-01905-z
    DOI: 10.1007/s10957-021-01905-z
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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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