Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/314976 
Year of Publication: 
2024
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 100 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 509-534
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We investigate location problems where the optimal solution is found within the tropical convex hull of the given input points. Our initial focus is on geodesically star-convex sets, using the asymmetric tropical distance. We introduce the concept of tropically quasiconvex functions, which have sub-level sets with this shape, and are closely related to monotonic functions. Our findings demonstrate that location problems using tropically quasiconvex functions as distance measures will result in an optimal solution within the tropical convex hull of the input points. We also extend this result to cases where the input points are replaced with tropically convex sets. Finally, we explore the applications of our research in phylogenetics, highlighting the properties of consensus methods that arise from our class of location problems.
Subjects: 
Tropical convexity
Tropically quasiconvex function
Monotonic norms
Tropical Lp-norm
Tropically convex consensus trees
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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