Journal of Optimization Theory and Applications

, Volume 115, Issue 2, pp 283–314 | Cite as

The Fermat–Torricelli Problem in Normed Planes and Spaces

  • H. Martini
  • K.J. Swanepoel
  • G. Weiss


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.

Fermat–Torricelli problem Weber problem location science facilities location finite-dimensional normed spaces Minkowski spaces finite-dimensional Banach spaces 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • H. Martini
    • 1
  • K.J. Swanepoel
    • 2
  • G. Weiss
    • 3
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany
  2. 2.Department of Mathematics, Applied Mathematics, and AstronomyUniversity of South AfricaPretoriaSouth Africa
  3. 3.Institut für GeometrieTechnische Universität DresdenDresdenGermany

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