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Facility location in normed linear spaces

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We study the Fermat–Torricelli problem in the framework of normed linear spaces by using some ingredients of convex analysis and optimization. Several general formulations of the Fermat–Torricelli problem are presented. Sufficient conditions for the existence and uniqueness of the minimum point are formulated. Existence conditions for the minimum point are related to reflexivity assumptions on the normed space. Uniqueness conditions are related to strict convexity assumptions on the normed space. In the second part of the paper we study the Fermat problem subject to constraints in the plane and on the sphere.

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Authors and Affiliations

  1. Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie No. 13, 050711, Bucharest, Romania

    Sorin Rădulescu

  2. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Diana-Olimpia Alexandrescu

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Vicenţiu D. Rădulescu

  4. Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Vicenţiu D. Rădulescu

Authors
  1. Sorin Rădulescu
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  2. Diana-Olimpia Alexandrescu
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  3. Vicenţiu D. Rădulescu
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Correspondence to Vicenţiu D. Rădulescu.

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Rădulescu, S., Alexandrescu, DO. & Rădulescu, V.D. Facility location in normed linear spaces. Optim Lett 9, 1353–1369 (2015). https://doi.org/10.1007/s11590-015-0846-y

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