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

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

Abstract

Integrals of optimal values of random linear programming problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Uniform convergence of the approximations is proved under fairly broad conditions allowing non-convex or discontinuous dependence on the parameter value and random size of the linear programming problem.

Suggested Citation

  • G.C. Pflug & A. Ruszczynski & R. Schultz, 1995. "On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse," Working Papers wp95003, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp95003
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    References listed on IDEAS

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    1. Alexander Shapiro, 1993. "Asymptotic Behavior of Optimal Solutions in Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 829-845, November.
    2. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    3. 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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