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Issue ESAIM: PROC
Volume 13, 2003
Proceedings of 2003 MODE-SMAI Conference
Page(s) 65 - 73
DOI 10.1051/proc:2003003

ESAIM: Proc., December 2003, Vol. 13, pp. 65-73
DOI: 10.1051/proc:2003003

Monte Carlo sampling approach to stochastic programming

A. Shapiro

School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA


Abstract
Various stochastic programming problems can be formulated as problems of optimization of an expected value function. Quite often the corresponding expectation function cannot be computed exactly and should be approximated, say by Monte Carlo sampling methods. In fact, in many practical applications, Monte Carlo simulation is the only reasonable way of estimating the expectation function. We discuss converges properties of the sample average approximation (SAA) approach to stochastic programming. We argue that the SAA method is easily implementable and can be surprisingly efficient for some classes of stochastic programming problems.


Mathematics Subject Classification. 90C15

Key words: stochastic programming, two and multi-stage stochastic programs, sample average approximation, Monte Carlo sampling, consistency, asymptotic normality, large deviations theory, validation analysis


© EDP Sciences, ESAIM 2003


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