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Tropical Fermat-Weber Polytropes by Sabol, John; Barnhill, David; Yoshida, Ruriko; Miura, Keiji is a scholarly article available to read on EtoBox.

What is Tropical Fermat-Weber Polytropes about?

We study the geometry of tropical Fermat-Weber points in terms of the symmetric tropical metric over the tropical projective torus. It is well-known that a tropical Fermat-Weber point of a given sample is not unique and we show that the set of all possible Fermat-Weber points forms a polytrope. To prove this, we show that the tropical Fermat-Weber polytrope is a bounded cell of a tropical hyperplane arrangement given by both max- and min-tropical hyperplanes with apices given by the sample. We also define tropical Fermat-Weber gradients and provide a gradient descent algorithm that converges to the Fermat-Weber polytrope.

Author

Sabol, John; Barnhill, David; Yoshida, Ruriko; Miura, Keiji

Published

2024

Language

EN