A convex Hull algorithm for solving a location problem
RAIRO - Operations Research - Recherche Opérationnelle, Volume 49 (2015) no. 3, pp. 589-600.

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.

Received:
Accepted:
DOI: 10.1051/ro/2014058
Classification: 52A20, 90C27
Keywords: Location problem, distance geometry, convex hull, Quickhull algorithm, subgradient method
Linh, Nguyen Kieu 1; Muu, Le Dung 2

1 Thai Nguyen University, Tan Thinh, Thai Nguyen, Vietnam.
2 Institute of Mathematics VAST, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam.
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Linh, Nguyen Kieu; Muu, Le Dung. A convex Hull algorithm for solving a location problem. RAIRO - Operations Research - Recherche Opérationnelle, Volume 49 (2015) no. 3, pp. 589-600. doi : 10.1051/ro/2014058. http://archive.numdam.org/articles/10.1051/ro/2014058/

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