Please use this identifier to cite or link to this item: https://doi.org/10.1287/moor.1070.0260
Title: Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints
Authors: Xu, H.
Meng, F. 
Keywords: Random set-valued mappings
Sample average approximations
Stationary points
Strong law of large numbers
Issue Date: Aug-2007
Citation: Xu, H., Meng, F. (2007-08). Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints. Mathematics of Operations Research 32 (3) : 648-668. ScholarBank@NUS Repository. https://doi.org/10.1287/moor.1070.0260
Abstract: In this paper we discuss the sample average approximation (SAA) method for a class of stochastic programs with nonsmooth equality constraints. We derive a uniform Strong Law of Large Numbers for random compact set-valued mappings and use it to investigate the convergence of Karush-Kuhn-Tucker points of SAA programs as the sample size increases. We also study the exponential convergence of global minimizers of the SAA problems to their counterparts of the true problem. The convergence analysis is extended to a smoothed SAA program. Finally, we apply the established results to a class of stochastic mathematical programs with complementarity constraints and report some preliminary numerical test results. ©2007 INFORMS.
Source Title: Mathematics of Operations Research
URI: http://scholarbank.nus.edu.sg/handle/10635/112988
ISSN: 0364765X
DOI: 10.1287/moor.1070.0260
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