Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/307629 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 86 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 393-415
Publisher: 
Springer US, New York, NY
Abstract: 
This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously considering α-approximations for all closed convex ordering cones of a fixed inner angle  γ∈π2,π, an approximation guarantee between  αand  2αis achieved, which depends continuously on  γ. The analysis is best-possible for any inner angle and it generalizes and unifies the known results that the set of supported solutions is a 2-approximation and that the efficient set itself is a 1-approximation. Moreover, it is shown that, for maximization problems, no approximation guarantee is achievable in general by considering larger ordering cones in the described fashion, which again generalizes a known result about the set of supported solutions.
Subjects: 
Multiobjective optimization
Approximate Pareto set
Ordering cone
Supported solution
Efficient solution
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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