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A Prediction–Correction ADMM for Multistage Stochastic Variational Inequalities

Author

Listed:
  • Ze You

    (Sichuan Normal University)

  • Haisen Zhang

    (Sichuan Normal University)

Abstract

The multistage stochastic variational inequality is reformulated into a variational inequality with separable structure through introducing a new variable. The prediction–correction ADMM which was originally proposed in He et al. (J Comput Math 24:693–710, 2006) for solving deterministic variational inequalities in finite-dimensional spaces is adapted to solve the multistage stochastic variational inequality. Weak convergence of the sequence generated by that algorithm is proved under the conditions of monotonicity and Lipschitz continuity. When the sample space is a finite set, the corresponding multistage stochastic variational inequality is actually defined on a finite-dimensional Hilbert space and the strong convergence of the algorithm naturally holds true. Some numerical examples are given to show the efficiency of the algorithm.

Suggested Citation

  • Ze You & Haisen Zhang, 2023. "A Prediction–Correction ADMM for Multistage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 693-731, November.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02296-z
    DOI: 10.1007/s10957-023-02296-z
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    References listed on IDEAS

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    1. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    2. Jie Sun & Xinmin Yang & Qiang Yao & Min Zhang, 2017. "Risk Minimization, Regret Minimization and Progressive Hedging Algorithms," Papers 1705.00340, arXiv.org, revised Jun 2020.
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