2025/03/13 by Comăneci, Andrei
#300 Sozialwissenschaften::330 Wirtschaft::330 Wirtschaft #500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik #Tropical L p-norm #Tropically convex consensus trees #monotonic norms #tropical convexity #tropically quasiconvex function
paper · doi:10.14279/depositonce-22622
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.