Circumscribed Spheres via Semi-infinite Optimization
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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