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Zbl 1186.90083
Xu, Huifu
Sample average approximation methods for a class of stochastic variational inequality problems. (English)
[J] Asia-Pac. J. Oper. Res. 27, No. 1, 103-119 (2010). ISSN 0217-5959; ISSN 1793-7019/e

Summary: We apply the well known sample average approximation (SAA) method to solve a class of stochastic variational inequality problems (SVIPs). We investigate the existence and convergence of a solution to the sample average approximated SVIP. Under some moderate conditions, we show that the sample average approximated SVIP has a solution with probability one and with probability approaching one exponentially fast with the increase of sample size, the solution converges to its true counterpart. Finally, we apply the existence and convergence results to SAA method for solving a class of stochastic nonlinear complementarity problems and stochastic programs with stochastic constraints.

MSC 2000:: *90C15 Stochastic programming
49J40 Variational methods including variational inequalities
90C33 Complementarity problems

Keywords: stochastic variational inequality; stochastic complementarity problem; sample average approximation; exponential convergence

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Zentralblatt MATH Berlin [Germany]