Geodesic
A convex Hull algorithm for solving a location problem
Linh, Nguyen Kieu1 ; Muu, Le Dung2
1 Thai Nguyen University, Tan Thinh, Thai Nguyen, Vietnam.
2 Institute of Mathematics VAST, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 3, pp. 589-600

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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.

Reçu le :
Accepté le :
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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     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},
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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

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