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Stability in multistage stochastic programming

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Abstract

Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.

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Author notes

  1. Olga Fiedler

    Present address: Institut für Mathematik, Freie Universität Berlin, Arnimallee 2-6, D-14195, Berlin, Germany

Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität Berlin, D-10099, Berlin, Germany

    Olga Fiedler & Werner Römisch

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  1. Olga Fiedler
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  2. Werner Römisch
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Additional information

This research has been supported by the Schwerpunktprogramm “Anwendungsbezogene Optimierung und Steuerung” of the Deutsche Forschungsgemeinschaft.

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Fiedler, O., Römisch, W. Stability in multistage stochastic programming. Ann Oper Res 56, 79–93 (1995). https://doi.org/10.1007/BF02031701

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