CVaR-based formulation and approximation method for stochastic variational inequalities
Xiaojun Chen Guihua Lin
Numerical Algebra, Control & Optimization 2011, 1(1): 35-48 doi: 10.3934/naco.2011.1.35
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.
keywords: D-gap function Stochastic variational inequalities convergence. conditional value at risk smoothing approximation Monte Carlo sampling approximation

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