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Some Aspects of Stability in Stochastic Programming

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  • Rüdiger Schultz

Abstract

Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems. Copyright Kluwer Academic Publishers 2000

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  • Rüdiger Schultz, 2000. "Some Aspects of Stability in Stochastic Programming," Annals of Operations Research, Springer, vol. 100(1), pages 55-84, December.
    • Handle: RePEc:spr:annopr:v:100:y:2000:i:1:p:55-84:10.1023/a:1019258932012
    DOI: 10.1023/A:1019258932012
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    Cited by:

    1. Trine Kristoffersen, 2005. "Deviation Measures in Linear Two-Stage Stochastic Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 255-274, November.
    2. Qingsong Duan & Mengwei Xu & Shaoyan Guo & Liwei Zhang, 2018. "Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    3. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    4. Marco Colombo & Andreas Grothey, 2013. "A decomposition-based crash-start for stochastic programming," Computational Optimization and Applications, Springer, vol. 55(2), pages 311-340, June.
    5. Narum, Benjamin S. & Fairbrother, Jamie & Wallace, Stein W., 2024. "Problem-based scenario generation by decomposing output distributions," European Journal of Operational Research, Elsevier, vol. 318(1), pages 154-166.
    6. 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.
    7. Johanna Burtscheidt & Matthias Claus, 2017. "A Note on Stability for Risk-Averse Stochastic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 298-308, January.

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