Minisum Hyperspheres in Normed Spaces

Mark-Christoph Körner ()
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Mark-Christoph Körner: Georg-August-Universität Göttingen

Chapter Chapter 3 in Minisum Hyperspheres, 2011, pp 37-57 from Springer

Abstract: Abstract This chapter deals with the minisum hypersphere problem in a finite dimensional real Banach space. Similar to Chapter 2, the existence of optimal solutions and incidence properties are discussed. A main topic of this Chapter is the case of polyhedral norms. It is shown that for polyhedral norms a minisum hypersphere always exists. For the planar case a geometric description of optimal solutions under polyhedral norms is given. Furthermore, a finite dominating set and algorithmic approaches are presented.

Keywords: Unit Ball; Normed Space; Euclidean Norm; Direction Line; Median Property (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9807-1_3

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DOI: 10.1007/978-1-4419-9807-1_3

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