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Title: CVAR-based formulation and approximation method for stochastic variational inequalities
Authors: Chen, X 
Lin, G
Keywords: Conditional value at risk
D-gap function
Monte Carlo sampling approximation
Smoothing approximation
Stochastic variational inequalities
Issue Date: 2011
Source: Numerical algebra, control and optimization, 2011, v. 1, no. 1, p. 35-48 How to cite?
Journal: Numerical Algebra, Control and Optimization 
Abstract: In this paper, we study the stochastic variational inequality problem (SVIP) from a viewpoint of minimization of conditional value-at-risk. We employ the D-gap residual function for VIPs to define a loss function for SVIPs. In order to reduce the risk of high losses in applications of SVIPs, we use the D-gap function and conditional value-at-risk to present a deterministic minimization reformulation for SVIPs. We show that the new reformulation is a convex program under suitable conditions. Furthermore, by using the smoothing techniques and the Monte Carlo methods, we propose a smoothing approximation method for finding a solution of the new reformulation and show that this method is globally convergent with probability one.
ISSN: 2155-3289
DOI: 10.3934/naco.2011.1.35
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