SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS

Huifu Xu ()
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Huifu Xu: School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

Asia-Pacific Journal of Operational Research (APJOR), 2010, vol. 27, issue 01, 103-119

Abstract: In this paper 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.

Keywords: Stochastic variational inequality; stochastic complementarity problem; sample average approximation; exponential convergence (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (18)

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DOI: 10.1142/S0217595910002569

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