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A unified approach to inverse robust optimization problems

Author

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  • Holger Berthold

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Till Heller

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Tobias Seidel

    (Fraunhofer Institute for Industrial Mathematics ITWM)

Abstract

A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. The reverse view is to first set a budget for the price one is willing to pay and then find the most robust solution. In this article, we aim to unify these inverse approaches to robustness. We provide a general problem definition and a proof of the existence of its solution. We study properties of this solution such as closedness, convexity, and boundedness. We also provide a comparison with existing robustness concepts such as the stability radius, the resilience radius, and the robust feasibility radius. We show that the general definition unifies these approaches. We conclude with an example that demonstrates the flexibility of the introduced concept.

Suggested Citation

  • Holger Berthold & Till Heller & Tobias Seidel, 2024. "A unified approach to inverse robust optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(1), pages 115-139, April.
    • Handle: RePEc:spr:mathme:v:99:y:2024:i:1:d:10.1007_s00186-023-00844-x
    DOI: 10.1007/s00186-023-00844-x
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    References listed on IDEAS

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    Cited by:

    1. Miguel A. Goberna & Vaithilingam Jeyakumar & Guoyin Li, 2024. "The Stability of Robustness for Conic Linear Programs with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1509-1530, November.

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