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Minisum Hyperspheres in Normed Spaces

In: Minisum Hyperspheres

Author

Listed:
  • Mark-Christoph Körner

    (Georg-August-Universität Göttingen)

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.

Suggested Citation

  • Mark-Christoph Körner, 2011. "Minisum Hyperspheres in Normed Spaces," Springer Optimization and Its Applications, in: Minisum Hyperspheres, chapter 0, pages 37-57, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9807-1_3
    DOI: 10.1007/978-1-4419-9807-1_3
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