Abstract
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 ℝn. 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.
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© 1992 Springer-Verlag Berlin Heidelberg
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Durier, R. (1992). A General Framework for the One Center Location Problem. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_29
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DOI: https://doi.org/10.1007/978-3-642-51682-5_29
Publisher Name: Springer, Berlin, Heidelberg
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