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Local convexity results in a generalized Fermat-Weber problem

โœ Scribed by J. Brimberg; R.F. Love

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
646 KB
Volume
37
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

A generalized form of the Fermat-Weber problem requires finding a point in R ~ to minimize a sum of nondecreasing functions of distances to m given points. In this paper, local convexity properties are investigated for the generalized problem. Sufficient conditions are derived which guarantee that the Hessian matrix of the objective function will be positive definite. The analysis also reveals that Weiszfeld-type iterative algorithms may have sublinear convergence rates, since the Hessian may only be positive semidefinite at a local minimum.

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