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On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Author

Listed:
  • Georg Pflug
  • Andrzej Ruszczyński
  • Rüdiger Schultz

Abstract

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established. Copyright Physica-Verlag 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:1:p:39-49
    DOI: 10.1007/BF01193835
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    References listed on IDEAS

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    1. SCHULTZ, Rüdiger & STOUGIE, Leen & van der VLERK, Maarten, 1995. "Solving Stochastic Programs with Complete Integer Recourse : A Framework Using Gröbner Bases," LIDAM Discussion Papers CORE 1995062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
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    Cited by:

    1. Andreas Eichhorn & Werner Römisch, 2007. "Stochastic Integer Programming: Limit Theorems and Confidence Intervals," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 118-135, February.
    2. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.

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