Asymptotic of an optimal location problem
type: Item
instance of: scholarly article
title: Asymptotic of an optimal location problem
zbMATH Open document ID: 1041.90025
DOI: 10.1016/S1631-073X(02)02575-X
author: Mahadevan Rajesh
author: Guy Bouchitté
author: Chloé Jimenez
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-06-16T00:00:00Z
review text: It is known that for a uniform demand density on the unit \(d\)-cube the minimum mean distance to the closest of \(n\) points, asymptotically equals \(C_dn^{-1/d}\). In particular \(C_2\) is known to be the average distance to the center for a uniform hexagon of unit area. In this paper the asymptotic result is extended to non uniform unit density \(f\), yielding the same value multiplied by \((\int f^p(x)\,dx)^{1/p}\) with \(p=d/(d+1)\).
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 90B85
Mathematics Subject Classification ID: 91B72
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 1850813
zbMATH Keywords: Mass transportation
zbMATH Keywords: Wasserstein distance
zbMATH Keywords: \(\Gamma\)-convergence
MaRDI profile type: Publication
cites work: Hexagonal Economic Regions Solve the Location Problem
cites work: New lower semicontinuity results for nonconvex functionals defined on measures
cites work: Integral representation of convex functions on a space of measures
cites work: Q4432366
cites work: An introduction to \(\Gamma\)-convergence
full work available at URL: s1631-073x(02)02575-x
OpenAlex ID: W2040771822
description: scientific article; zbMATH DE number 1850813