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.

Accepted:

DOI: 10.1051/ro/2014058

Keywords: Location problem, distance geometry, convex hull, Quickhull algorithm, subgradient method

^{1}; Muu, Le Dung

^{2}

@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://archive.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://archive.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://archive.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, 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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