Locating a general minisum ‘circle’ on the plane

Locating a general minisum ‘circle’ on the plane

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Article ID: iaor201113451
Volume: 9
Issue: 4
Start Page Number: 351
End Page Number: 370
Publication Date: Dec 2011
Journal: 4OR
Authors: , , ,
Keywords: optimization, heuristics
Abstract:

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.

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