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The Fermat-Torricelli problem in normed planes and spaces

Martini, Horst, Swanepoel, Konrad ORCID: 0000-0002-1668-887X and Weiss, Gunter (2002) The Fermat-Torricelli problem in normed planes and spaces. Journal of Optimization Theory and Applications, 115 (2). pp. 283-314. ISSN 0022-3239

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Identification Number: 10.1023/A:1020884004689


We investigate the Fermat–Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat–Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat–Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach.

Item Type: Article
Official URL:
Additional Information: © 2002 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Oct 2009 09:36
Last Modified: 11 Apr 2024 02:03

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