Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints
Xu, Huifu and Meng, Fanwen (2007) 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. (doi:10.1287/moor.1070.0260).
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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.
|Digital Object Identifier (DOI):||doi:10.1287/moor.1070.0260|
|Keywords:||sample average approximations, strong law of large numbers, random set-valued mappings, stationary points|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||17 Mar 2010|
|Last Modified:||06 Aug 2015 02:59|
Stochastic Mathematical Programs with Equilibrium Constraints
Funded by: EPSRC (GR/S90850/01)
11 October 2004 to 10 October 2006
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