On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions
Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.
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- Lucchetti, R. & Salinetti, G. & Wets, R. J. B., 1994. "Uniform Convergence of Probability Measures: Topological Criteria," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 252-264, November.
- Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, EconWPA, revised 13 Nov 2003.
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