Convergence Properties of Two-Stage Stochastic Programming

L. Dai, C. H. Chen and John Birge
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L. Dai: Genuity
C. H. Chen: University of Pennsylvania

Journal of Optimization Theory and Applications, 2000, vol. 106, issue 3, No 3, 489-509

Abstract: Abstract This paper considers a procedure of two-stage stochastic programming in which the performance function to be optimized is replaced by its empirical mean. This procedure converts a stochastic optimization problem into a deterministic one for which many methods are available. Another strength of the method is that there is essentially no requirement on the distribution of the random variables involved. Exponential convergence for the probability of deviation of the empirical optimum from the true optimum is established using large deviation techniques. Explicit bounds on the convergence rates are obtained for the case of quadratic performance functions. Finally, numerical results are presented for the famous news vendor problem, which lends experimental evidence supporting exponential convergence.

Keywords: stochastic programming; stochastic optimization; sample paths; convergence rates; empirical means (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (22)

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DOI: 10.1023/A:1004649211111

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