Convergence properties of two-stage stochastic programming

Convergence properties of two-stage stochastic programming

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Article ID: iaor2002474
Country: United States
Volume: 106
Issue: 3
Start Page Number: 489
End Page Number: 509
Publication Date: Sep 2000
Journal: Journal of Optimization Theory and Applications
Authors: , ,
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.

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