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

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074, Würzburg, Germany

    Simone Görner & Christian Kanzow

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  1. Simone Görner
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  2. Christian Kanzow
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Correspondence to Christian Kanzow.

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Communicated by Horst Martini.

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Görner, S., Kanzow, C. On Newton’s Method for the Fermat–Weber Location Problem. J Optim Theory Appl 170, 107–118 (2016). https://doi.org/10.1007/s10957-016-0946-6

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  • DOI: https://doi.org/10.1007/s10957-016-0946-6

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