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The Fermat–Torricelli Problem in Normed Planes and Spaces

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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.

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany

    H. Martini (Professor)

  2. Department of Mathematics, Applied Mathematics, and Astronomy, University of South Africa, Pretoria, South Africa

    K.J. Swanepoel (Associate Professor)

  3. Institut für Geometrie, Technische Universität Dresden, Dresden, Germany

    G. Weiss (Professor)

Authors
  1. H. Martini
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  2. K.J. Swanepoel
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  3. G. Weiss
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Martini, H., Swanepoel, K. & Weiss, G. The Fermat–Torricelli Problem in Normed Planes and Spaces. Journal of Optimization Theory and Applications 115, 283–314 (2002). https://doi.org/10.1023/A:1020884004689

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