Qualitative Properties of $k-$Center Problems
Optimization and Control
2024-09-19 v1
Abstract
In this paper, we study generalized versions of the k-center problem, which involves finding k circles of the smallest possible equal radius that cover a finite set of points in the plane. By utilizing the Minkowski gauge function, we extend this problem to generalized balls induced by various convex sets in finite dimensions, rather than limiting it to circles in the plane. First, we establish several fundamental properties of the global optimal solutions to this problem. We then introduce the notion of local optimal solutions and provide a sufficient condition for their existence. We also provide several illustrative examples to clarify the proposed problems.
Cite
@article{arxiv.2409.12091,
title = {Qualitative Properties of $k-$Center Problems},
author = {Vo Si Trong Long and Nguyen Mau Nam and Jacob Sharkansky and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2409.12091},
year = {2024}
}