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An Extension of the Fermat-Torricelli Problem

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  • T. V. Tan

    (Hanoi National University of Education)

Abstract

The Fermat-Torricelli problem is an optimization problem associated with a finite subset $\{a_{j}\}_{j=1}^{q}$ of ℝ N and a family $\{c_{j}\}_{j=1}^{q}$ of positive weights. The function F to be minimized is defined by $F(x)=\sum _{j=1}^{q}c_{j}\Vert x-a_{j}\Vert$ . In this paper, we extend this problem to the case of volumes.

Suggested Citation

  • T. V. Tan, 2010. "An Extension of the Fermat-Torricelli Problem," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 735-744, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9686-1
    DOI: 10.1007/s10957-010-9686-1
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    References listed on IDEAS

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    1. H. Martini & K.J. Swanepoel & G. Weiss, 2002. "The Fermat–Torricelli Problem in Normed Planes and Spaces," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 283-314, November.
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    Cited by:

    1. Boris Mordukhovich & Nguyen Mau Nam, 2011. "Applications of Variational Analysis to a Generalized Fermat-Torricelli Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 431-454, March.
    2. Nguyen Mau Nam & Nguyen Hoang & Nguyen Thai An, 2014. "Constructions of Solutions to Generalized Sylvester and Fermat–Torricelli Problems for Euclidean Balls," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 483-509, February.
    3. Yaakov S. Kupitz & Horst Martini & Margarita Spirova, 2013. "The Fermat–Torricelli Problem, Part I: A Discrete Gradient-Method Approach," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 305-327, August.
    4. Simeon Reich & Truong Minh Tuyen, 2023. "The Generalized Fermat–Torricelli Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 78-97, January.

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