6533b858fe1ef96bd12b6c60
RESEARCH PRODUCT
A General Framework for the One Center Location Problem
Roland Duriersubject
CombinatoricsMonotone polygonOptimization problemMixed normNorm (mathematics)Real vectorPositive weightDual normMathematicsdescription
This paper deals with an optimization problem where the objective function F is defined on a real vector space X by F(x) = γ(w 1║x - a 1║1, ⋯, w n ║x - a n║ n ), a formula in which a 1, ⋯, a n are n given points in X, ║∙║1, ⋯, ║∙║ n n norms on X, w 1, ⋯, w n positive numbers and γ a monotone norm on ℝ n . A geometric description of the set of optimal solutions to the problem min F(x) is given, illustrated by some examples. When all norms ║∙║i are equal, and γ being successively the l 1 , l ∞ and l 2-norm, a particular study is made, which shows the peculiar role played by the l 1-norm.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-01-01 |