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Title: Regularized mathematical programs with stochastic equilibrium constraints : estimating structural demand models
Authors: Chen, X 
Sun, H
Wets, RJB
Keywords: Graphical convergence
Monotone linear complementarity problem
Sample average approximation
Stochastic equilibrium
Issue Date: 2015
Publisher: Society for Industrial and Applied Mathematics Publications
Source: SIAM Journal on optimization, 2015, v. 25, no. 1, p. 53-75 How to cite?
Journal: SIAM Journal on Optimization 
Abstract: The article considers a particular class of optimization problems involving set-valued stochastic equilibrium constraints. We develop a solution procedure that relies on an approximation scheme for the equilibrium constraints. Based on regularization, we replace the approximated equilibrium constraints by those involving only single-valued Lipschitz continuous functions. In addition, sampling has the further effect of replacing the "simplified" equilibrium constraints by more manageable ones obtained by implicitly discretizing the (given) probability measure so as to render the problem computationally tractable. Convergence is obtained by relying, in particular, on the graphical convergence of the approximated equilibrium constraints. The problem of estimating the characteristics of a demand model, a widely studied problem in microeconometrics, serves both as motivation and illustration of the regularization and sampling procedure.
ISSN: 1674-4926
DOI: 10.1137/130930157
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