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Optimal selectors for stochastic linear programs

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Abstract

The “distribution problem” of stochastic linear programming consists in answering the following two questions: Is the optimal value of a given stochastic linear program—regarded as a function—measurable, and if so, what is its distribution?

In the present note we make use of a general selection theorem to answer the first question positively. By this approach, an answer to the second question is obtained—at least theoretically—at the same time.

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References

  1. P. Kall,Stochastic Linear Programming, Springer-Verlag, Berlin, 1976.

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  2. M. Schäl, A Selection Theorem for Optimization Problems.Archiv der Mathematik,XXV (1974) 219–224.

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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Hamburg, Bundesstrasse 55, 2000, Hamburg 13, Germany

    Wolf-Rüdiger Heilmann

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  1. Wolf-Rüdiger Heilmann
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Communicated by J. Stoer

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Heilmann, WR. Optimal selectors for stochastic linear programs. Appl Math Optim 4, 139–142 (1977). https://doi.org/10.1007/BF01442136

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  • DOI: https://doi.org/10.1007/BF01442136

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