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.
Accepté le :
DOI : 10.1051/ro/2014058
Mots-clés : Location problem, distance geometry, convex hull, Quickhull algorithm, subgradient method
@article{RO_2015__49_3_589_0,
author = {Linh, Nguyen Kieu and Muu, Le Dung},
title = {A convex {Hull} algorithm for solving a location problem},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {589--600},
publisher = {EDP-Sciences},
volume = {49},
number = {3},
year = {2015},
doi = {10.1051/ro/2014058},
mrnumber = {3349136},
zbl = {1321.52001},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2014058/}
}
TY - JOUR AU - Linh, Nguyen Kieu AU - Muu, Le Dung TI - A convex Hull algorithm for solving a location problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 589 EP - 600 VL - 49 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2014058/ DO - 10.1051/ro/2014058 LA - en ID - RO_2015__49_3_589_0 ER -
%0 Journal Article %A Linh, Nguyen Kieu %A Muu, Le Dung %T A convex Hull algorithm for solving a location problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 589-600 %V 49 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2014058/ %R 10.1051/ro/2014058 %G en %F RO_2015__49_3_589_0
Linh, Nguyen Kieu; Muu, Le Dung. A convex Hull algorithm for solving a location problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 3, pp. 589-600. doi : 10.1051/ro/2014058. http://www.numdam.org/articles/10.1051/ro/2014058/
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