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Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming

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  • Min Li

    (Beijing Jiaotong University)

  • Chao Zhang

    (Beijing Jiaotong University)

Abstract

We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the two problems is shown under some moderate conditions, and the monotonicity of the two-stage stochastic variational inequality is discussed under additional conditions. We provide a discretization scheme with convergence results and employ the progressive hedging method with double parameterization to solve the discretized stochastic variational inequality. As an application, we show how the water resources management problem under uncertainty can be transformed from a two-stage stochastic programming problem to a two-stage stochastic variational inequality, and how to solve it, using the discretization scheme and the progressive hedging method with double parameterization.

Suggested Citation

  • Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01686-x
    DOI: 10.1007/s10957-020-01686-x
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    References listed on IDEAS

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    4. 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.
    5. Lang Zhao & Yuan Zeng & Zhidong Wang & Yizheng Li & Dong Peng & Yao Wang & Xueying Wang, 2023. "Robust Optimal Scheduling of Integrated Energy Systems Considering the Uncertainty of Power Supply and Load in the Power Market," Energies, MDPI, vol. 16(14), pages 1-14, July.

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