| Issue |
RAIRO-Oper. Res.
Volume 49, Number 3, July-September 2015
|
|
|---|---|---|
| Page(s) | 589 - 600 | |
| DOI | https://doi.org/10.1051/ro/2014058 | |
| Published online | 23 February 2015 | |
A convex Hull algorithm for solving a location problem∗
1 Thai Nguyen University, Tan Thinh, Thai Nguyen, Vietnam.
nguyenkieulinhk4@gmail.com
2 Institute of Mathematics VAST, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam.
ldmuu@math.ac.vn
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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