A unified approach to inverse robust optimization problems

Holger Berthold (), Till Heller () and Tobias Seidel ()
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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

Mathematical Methods of Operations Research, 2024, vol. 99, issue 1, No 6, 115-139

Abstract: 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.

Keywords: Robust optimization; Uncertainty sets; Non-linear optimization; Price of robustness; GSIP (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00186-023-00844-x

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