Abstract
The General Fermat Problem asks for the minimum of the weighted sum of distances fromm points inn-space. Dozens of papers have been written on variants of this problem and most of them have merely reproduced known results. This note calls attention to the work of Weiszfeld in 1937, who may have been the first to propose an iterative algorithm. Although the same algorithm has been rediscovered at least three times, there seems to be no completely correct treatment of its properties in the literature. Such a treatment, including a proof of convergence, is the sole object of this note. Other aspects of the problem are given scant attention.
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This paper was written while the author was Science Faculty Fellow of the National Science Foundation at the London School of Economics.
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Kuhn, H.W. A note on Fermat's problem. Mathematical Programming 4, 98–107 (1973). https://doi.org/10.1007/BF01584648
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DOI: https://doi.org/10.1007/BF01584648