Sample average approximation methods for a class of stochastic variational inequality problems
Sample average approximation methods for a class of stochastic variational inequality problems
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
stochastic variational inequality, stochastic complementarity problem, sample average approximation, exponential convergence
103-119
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
February 2010
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Xu, Huifu
(2010)
Sample average approximation methods for a class of stochastic variational inequality problems.
Asia-Pacific Journal of Operational Research, 27 (1), .
(doi:10.1142/S0217595910002569).
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
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Published date: February 2010
Keywords:
stochastic variational inequality, stochastic complementarity problem, sample average approximation, exponential convergence
Organisations:
Operational Research
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Local EPrints ID: 145461
URI: http://eprints.soton.ac.uk/id/eprint/145461
ISSN: 0217-5959
PURE UUID: 2cddffcf-344e-4c23-9e4b-1a15ecb8ae64
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Date deposited: 22 Apr 2010 10:20
Last modified: 14 Mar 2024 02:47
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Author:
Huifu Xu
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