Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5953
Title: Stochastic variational inequalities : residual minimization smoothing sample average approximations
Authors: Chen, X 
Wets, RJ
Zhang, Y
Keywords: Stochastic variational inequalities
Epi-convergence
Lower semicontinuous
Upper semicontinuous
Semismooth
Smoothing sample average approximation
Expected residual minimization
Stationary point
Issue Date: 2012
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2012, v. 22, no. 2, p. 649–673 How to cite?
Journal: SIAM Journal on optimization 
Abstract: The stochastic variational inequality (VI) has been used widely in engineering and economics as an effective mathematical model for a number of equilibrium problems involving uncertain data. This paper presents a new expected residual minimization (ERM) formulation for a class of stochastic VI. The objective of the ERM-formulation is Lipschitz continuous and semismooth which helps us guarantee the existence of a solution and convergence of approximation methods. We propose a globally convergent (a.s.) smoothing sample average approximation (SSAA) method to minimize the residual function; this minimization problem is convex for the linear stochastic VI if the expected matrix is positive semidefinite. We show that the ERM problem and its SSAA problems have minimizers in a compact set and any cluster point of minimizers and stationary points of the SSAA problems is a minimizer and a stationary point of the ERM problem (a.s.). Our examples come from applications involving traffic flow problems. We show that the conditions we impose are satisfied and that the solutions, efficiently generated by the SSAA procedure, have desirable properties.
URI: http://hdl.handle.net/10397/5953
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/110825248
Rights: © 2012 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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