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Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming

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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.

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Acknowledgements

The authors would like to thank the associate editor and the anonymous referees for valuable suggestions. The authors would like to thank Prof. Jie Sun of Curtin University who encourages us to consider this topic and provides the MATLAB code of PHM for solving stochastic linear complementarity problem in [15]. The work is supported in part by “the Fundamental Research Funds for the Central Universities” (Grant No. 2018YJS184) and “the National Natural Science Foundation of China” (Grant No. 11571033, 11431002).

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  1. Beijing Jiaotong University, Beijing, China

    Min Li & Chao Zhang

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  1. Min Li
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  2. Chao Zhang
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Correspondence to Chao Zhang.

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Communicated by Nguyen Dong Yen.

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Li, M., Zhang, C. Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming. J Optim Theory Appl 186, 324–343 (2020). https://doi.org/10.1007/s10957-020-01686-x

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