Abstract
In this chapter we analyze the behavior of Weiszfeld’s method for solving the Fermat–Weber location problem. We show that the algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.
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References
Beck A, Sabach S (2015) Weiszfeld’s method: old and new results. J Optim Theory Appl 164:1–40
Mordukhovich BS, Nam NM (2014) An easy path to convex analysis and applications. Morgan&Clayton Publishes, San Rafael, CA
Weiszfeld EV (1937) Sur le point pour lequel la somme des distances de n points donnes est minimum. Tohoku Math J 43:355–386
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© 2016 Springer International Publishing Switzerland
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Zaslavski, A.J. (2016). Weiszfeld’s Method. In: Numerical Optimization with Computational Errors. Springer Optimization and Its Applications, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-30921-7_6
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DOI: https://doi.org/10.1007/978-3-319-30921-7_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30920-0
Online ISBN: 978-3-319-30921-7
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