On the location of the minimum point in the Euclidean distance sum problem
type: Item
instance of: scholarly article
title: On the location of the minimum point in the Euclidean distance sum problem
zbMATH Open document ID: 1396.52017
author: Luis Fernando Mello
author: Lucas Ruiz dos Santos
published in: São Paulo Journal of Mathematical Sciences
publication date: 2018-07-31T00:00:00Z
review text: Necessary and sufficient conditions on the location of the minimum point in the Euclidean distance sum problem (i.e. the the problem of minimizing the sum of distances to \(n\) given points) are provided and proven by analytical methods that, as the authors assert, do not rely on previous contributions in this direction. Hints towards further developments are presented in the concluding section.
reviewed by: Sorin-Mihai Grad
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 26B12
zbMATH DE Number: 6911819
zbMATH Keywords: generalized ellipse
zbMATH Keywords: minimum point
zbMATH Keywords: focal point
zbMATH Keywords: distance function
zbMATH Keywords: convex function
zbMATH Keywords: Euclidean distance-sum problem
MaRDI profile type: Publication
full work available at URL: s40863-017-0061-0
OpenAlex ID: W2726506814
Wikidata QID: Q108075139
cites work: A note on Fermat's problem
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cites work: On a lower and upper bound for the curvature of ellipses with more than two foci
cites work: Q5767400
DOI: 10.1007/S40863-017-0061-0
description: scientific article; zbMATH DE number 6911819