Volume 49, Number 3, July-September 2015
|Page(s)||589 - 600|
|Published online||23 February 2015|
A convex Hull algorithm for solving a location problem∗
Received: 23 February 2014
Accepted: 12 November 2014
An important problem in distance geometry is of determining the position of an unknown point in a given convex set such that its longest distance to a set of finite number of points is shortest. In this paper we present an algorithm based on subgradient method and convex hull computation for solving this problem. A recent improvement of Quickhull algorithm for computing the convex hull of a finite set of planar points is applied to fasten up the computations in our numerical experiments.
Mathematics Subject Classification: 52A20 / 90C27
Key words: Location problem / distance geometry / convex hull / Quickhull algorithm / subgradient method
© EDP Sciences, ROADEF, SMAI, 2015
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