期刊
OPTIMIZATION
卷 57, 期 3, 页码 395-418出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331930801954177
关键词
stochastic programming; equilibrium constraints; Stackelberg-Nash-Cournot equilibrium; variational inequality; sample average approximation; exponential convergence; smoothing
In this article, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both - the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and generalized Karush-Kuhn-Tucker points of the SAA program to their true counterparts. We also study uniform exponential convergence of the sample average approximations, and as a consequence derive estimates of the sample size required to solve the true problem with a given accuracy. Finally, we present some preliminary numerical test results.
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