Journal of Global Optimization

, Volume 51, Issue 1, pp 115–132 | Cite as

Geometric fit of a point set by generalized circles

  • Mark-Christoph KörnerEmail author
  • Jack Brimberg
  • Henrik Juel
  • Anita Schöbel
Open Access


In our paper we approximate a set of given points by a general circle. More precisely, given two norms k 1 and k 2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k 1 such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k 2. We present results for the general case. In the case that k 1 and k 2 are both polyhedral norms, we are able to solve the problem by investigating a finite candidate set.


Circle location Dimensional facility Minisum Polyhedral norms 

Mathematics Subject Classification (2000)

62J02 65D10 90C26 90B85 97N50 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Mark-Christoph Körner
    • 1
    Email author
  • Jack Brimberg
    • 2
    • 3
  • Henrik Juel
    • 4
  • Anita Schöbel
    • 5
  1. 1.Institute for Numerical and Applied MathematicsGeorg-August-Universität GöttingenGöttingenGermany
  2. 2.Royal Military College of CanadaKingstonCanada
  3. 3.Groupe d’Études et de Recherche en Analyse des DécisionsMontréalCanada
  4. 4.Technical University of DenmarkLyngbyDenmark
  5. 5.Georg-August-Universität GöttingenGöttingenGermany

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