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On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions

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  • G.C. Pflug
  • A. Ruszczynski
  • R. Schultz

Abstract

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.

Suggested Citation

  • G.C. Pflug & A. Ruszczynski & R. Schultz, 1996. "On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions," Working Papers wp96020, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp96020
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    References listed on IDEAS

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    1. 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.
    2. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
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    Cited by:

    1. Georg Pflug & Andrzej Ruszczyński & Rüdiger Schultz, 1998. "On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 39-49, February.

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