Abstract
For two-stage stochastic programs with integrality constraints in the second stage, we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability measure.
Sufficient conditions for lower semicontinuity, continuity and Lipschitz continuity with respect to the first-stage policy are presented. Furthermore, joint continuity in the policy and the probability measure is established. This leads to conclusions on the stability of optimal values and optimal solutions to the two-stage stochastic program when subjecting the underlying probability measure to perturbations.
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This research is supported by the Schwerpunktprogramm “Anwendungsbezogene Optimierung und Steuerung” of the Deutsche Forschungsgemeinschaft.
The main part of the paper was written while the author was an assistant at the Department of Mathematics at Humboldt University Berlin.
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Schultz, R. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Mathematical Programming 70, 73–89 (1995). https://doi.org/10.1007/BF01585929
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DOI: https://doi.org/10.1007/BF01585929