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Title: Two-stage stochastic variational inequalities : an ERM-solution procedure
Authors: Chen, X 
Pong, TK 
Wets, RJB
Issue Date: Sep-2017
Source: Mathematical programming, Sept. 2017, v. 165, no. 1, p. 71-111
Abstract: We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas-Rachford splitting method for the corresponding two-stage stochastic programming with recourse.
Keywords: Stochastic variational inequalities
Stochastic program with recourse
Wardrop equilibrium
Expected residual minimization
Regularized gap function
Splitting method
Publisher: Springer
Journal: Mathematical programming 
ISSN: 0025-5610
EISSN: 1436-4646
DOI: 10.1007/s10107-017-1132-9
Rights: © Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
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