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arXiv · 2606.27503

Tropical Fermat--Weber Problems over Non-Finite Data and their Inverse Formulations

John Sabol·Ruriko Yoshida
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Abstract

The term tropical pseudonorm refers to a family of (not necessarily symmetric) gauge functions that arise in tropical or idempotent geometry. An important characteristic of these gauges is their invariance under translation by a constant vector, allowing them to descent naturally to tropical projective spaces. In this work, we explore the tropical one-infinity pseudonorm, a polyhedral hybrid gauge that allows for tunable asymmetry, in the context of a Fermat--Weber location problem. We extend previous formulations in considering non-finite data, and we investigate several variants of the inverse problem, providing linear programming formulations for their solution.

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John Sabol, Ruriko Yoshida. 2026-06-25. Tropical Fermat--Weber Problems over Non-Finite Data and their Inverse Formulations. https://arxiv.org/abs/2606.27503

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