Abstract
This chapter is devoted to the Euclidean version of the minisum hypersphere problem where hyperspheres are defined with respect to the Euclidean norm. A simple formula for the Euclidean distance between a point and a hypersphere is derived and the existence of optimal solutions is discussed in detail. Furthermore, incidence properties of optimal solutions to the minisum hypersphere problem are stated and illustrated in various examples. Finally, solution approaches for the planar case are presented.
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© 2011 Springer Science+Business Media, LLC
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Körner, MC. (2011). Euclidean Minisum Hyperspheres. In: Minisum Hyperspheres. Springer Optimization and Its Applications(), vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9807-1_2
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DOI: https://doi.org/10.1007/978-1-4419-9807-1_2
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9806-4
Online ISBN: 978-1-4419-9807-1
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