Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming

Min Li () and Chao Zhang ()
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Min Li: Beijing Jiaotong University
Chao Zhang: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 16, 324-343

Abstract: 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.

Keywords: Two-stage stochastic variational inequality; Stochastic programming; Discrete approximation; Water resources management under uncertainty; 49J53; 49K30; 90C15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-020-01686-x

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