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Circumscribed Spheres via Semi-infinite Optimization

  • Friedrich Juhnke
Conference paper

Abstract

In the paper the circumsphere of an arbitrarily given compact set K in the n-dimentional euclidean space Rn will be described 18 solution of a linear semi-infinite optimisation problem using the Minkokski support function. Applying the correspondiDg linear semi-infinite duality theory, we shall derive characteristic properties of the circumsphere as well as the inequality of Jung between diameter and circumradius. The Jung’s upper bound for the ratio of diameter and circumradius can be improved in special cases ill which there exists a degenerated optimal dual basic solution.

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References

  1. [1]
    Glashoff, K.; S. A. Gustafson: Linear Optimization and Approximation, Springer-Verlag New York 1983.CrossRefGoogle Scholar
  2. [2]
    John, F.: Extremum problems with inequalities as subsidiary conditions. Courant Anniversary Volume, Interscience, New York 1948, pp. 187–204.Google Scholar
  3. [3]
    Juhnke, F.: Das Umkugelproblem und lineare semiinfinite Optimierung, Beiträge zur Algebra und Geometrie 28 (1988), 147–156.Google Scholar
  4. [4]
    Santalo, L.A.: Convex regions on the n-dimensional spherical surface. Annals of Mathematics, vol. 47 (1946), 448–459.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Friedrich Juhnke
    • 1
  1. 1.Fakultät für MathematikTU MagdeburgMagdeburgGermany

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