Locating a general minisum ‘circle’ on the plane
- 106 Downloads
We approximate a set of given points in the plane by the boundary of a convex and symmetric set which is the unit circle of some norm. This generalizes previous work on the subject which considers Euclidean circles only. More precisely, we examine the problem of locating and scaling the unit circle of some given norm k with respect to given points on the plane such that the sum of weighted distances (as measured by the same norm k) between the circumference of the circle and the points is minimized. We present general results and are able to identify a finite dominating set in the case that k is a polyhedral norm.
KeywordsFacility location General norm Circle
MSC classification (2000)90B85 90C26 90C90
Unable to display preview. Download preview PDF.
- Brimberg J, Juel H, Schöbel A (2009a) Locating a circle on the plane using the minimax criterion. Stud Locat Anal 17: 45–60Google Scholar
- Körner M (2010) Minisum hyperspheres. Dissertation, Georg-August-Universität GöttingenGoogle Scholar
- Körner M, Brimberg J, Juel H, Schöbel A Geometric fit of a point set by generalized circles. J Glob Optim, to appearGoogle Scholar
- Ma L (2000) Bisectors and Voronoi Diagrams for convex distance functions. Dissertation, Fernuniversität Hagen. http://wwwpi6.fernuni-hagen.de/Publikationen/tr267
- Nickel S, Puerto J (2005) Location theory: a unified approach. Springer, BerlinGoogle Scholar
- Phelps RR (1989) Convex functions, monotone operators and differentiability. Lecture notes in mathematics 1364, Springer, BerlinGoogle Scholar
- Schöbel A (1999) Locating lines and hyperplanes. Kluwer, DordrechtGoogle Scholar
- Suzuki T (2005) Optimal location of orbital routes in a circular city. ISOLDE X, Sevilla and Islantilla, Spain, June 2-8Google Scholar