On the continuous Fermat-Weber problem for a convex polygon using Euclidean distance [article]

Thomas T.C.K. Zhang, John Gunnar Carlsson
2014 arXiv   pre-print
We consider the continuous Fermat-Weber problem, where the customers are continuously (uniformly) distributed along the boundary of a convex polygon. We derive the closed-form expression for finding the average distance from a given point to the continuously distributed customers along the boundary. A Weiszfeld-type procedure is proposed for this model, which is shown to be linearly convergent. We also derive a closed-form formula to find the average distance for a given point to the entire
more » ... ex polygon, assuming a uniform distribution. Since the function is smooth, convex, and explicitly given, the continuous version of the Fermat-Weber problem over a convex polygon can be solved easily by numerical algorithms.
arXiv:1403.3715v1 fatcat:wn5k4a5mkvfutjez4itcawzgjy