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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Glashoff, K.; S. A. Gustafson: Linear Optimization and Approximation, Springer-Verlag New York 1983.
John, F.: Extremum problems with inequalities as subsidiary conditions. Courant Anniversary Volume, Interscience, New York 1948, pp. 187–204.
Juhnke, F.: Das Umkugelproblem und lineare semiinfinite Optimierung, Beiträge zur Algebra und Geometrie 28 (1988), 147–156.
Santalo, L.A.: Convex regions on the n-dimensional spherical surface. Annals of Mathematics, vol. 47 (1946), 448–459.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Juhnke, F. (1993). Circumscribed Spheres via Semi-infinite Optimization. In: Karmann, A., Mosler, K., Schader, M., Uebe, G. (eds) Operations Research ’92. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12629-5_59
Download citation
DOI: https://doi.org/10.1007/978-3-662-12629-5_59
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0679-3
Online ISBN: 978-3-662-12629-5
eBook Packages: Springer Book Archive