# A note on Fermat's problem

@article{Kuhn1973ANO, title={A note on Fermat's problem}, author={Harold W. Kuhn}, journal={Mathematical Programming}, year={1973}, volume={4}, pages={98-107} }

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…

## 330 Citations

Local convergence in Fermat's problem

- MathematicsMath. Program.
- 1974

It is shown that although convergence is global, the rapidity of convergence depends strongly upon whether or not is a destination, and locally convergence is always linear with upper and lower asymptotic convergence boundsλ andλ′.

Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem

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- 1989

It is demonstrated that Kuhn's convergence theorem is not always correct and it is conjecture that if this algorithm is initiated at the affine subspace spanned by them given points, the convergence is ensured for all but a denumerable number of starting points.

A Note on Weighted Fermat Problem in Lp Space

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The Fermat-Weber problem is one of the most widely studied problems in classical location theory. In his previous work, Brimberg (1995) attempts to resolve a conjecture posed by Chandrasekaran and…

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In this chapter we are concerned with problems of the following type: Given a finite set of weighted points in Euclidean n-space, n ≥ 2, we are interested in the location of an additonal point such…

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- Mathematics
- 2003

The Fermat-Weber problem is one of the most widely studied problems in classical location theory. In his previous work, Brimberg (1995) attempts to resolve a conjecture posed by Chandrasekaran and…

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- MathematicsMath. Program.
- 1995

It is proved that Weiszfeld's algorithm converges to the unique optimal solution for all but a denumerable set of starting points if, and only if, the convex hull of the given points is of dimensionN.

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