Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/314962 
Year of Publication: 
2024
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 99 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 115-139
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Robust optimization
Uncertainty sets
Non-linear optimization
Price of robustness
GSIP
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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