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On Newton’s Method for the Fermat–Weber Location Problem

Author

Listed:
  • Simone Görner

    (University of Würzburg)

  • Christian Kanzow

    (University of Würzburg)

Abstract

This paper considers the Fermat–Weber location problem. It is shown that, after a suitable initialization, the standard Newton method can be applied to the Fermat–Weber problem, and is globally and locally quadratically convergent. A numerical comparison with the popular Weiszfeld algorithm shows that Newton’s method is significantly more efficient than the Weiszfeld scheme.

Suggested Citation

  • Simone Görner & Christian Kanzow, 2016. "On Newton’s Method for the Fermat–Weber Location Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 107-118, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0946-6
    DOI: 10.1007/s10957-016-0946-6
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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.
    2. 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.
    3. Thomas Jahn & Yaakov S. Kupitz & Horst Martini & Christian Richter, 2015. "Minsum Location Extended to Gauges and to Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 711-746, September.
    4. Amir Beck & Shoham Sabach, 2015. "Weiszfeld’s Method: Old and New Results," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 1-40, January.
    5. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, September.
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    Cited by:

    1. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    2. Frank Plastria, 2021. "Using the power of ideal solutions: simple proofs of some old and new results in location theory," 4OR, Springer, vol. 19(3), pages 449-467, September.

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