The Fermat–Torricelli Problem in Normed Planes and Spaces

H. Martini, K.J. Swanepoel and G. Weiss
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H. Martini: Technische Universität Chemnitz
K.J. Swanepoel: University of South Africa
G. Weiss: Technische Universität Dresden

Journal of Optimization Theory and Applications, 2002, vol. 115, issue 2, No 3, 283-314

Abstract: Abstract 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.

Keywords: Fermat–Torricelli problem; Weber problem; location science; facilities location; finite-dimensional normed spaces; Minkowski spaces; finite-dimensional Banach spaces (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/A:1020884004689

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