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Das Umkugelproblem und lineare semiinfinite Optimierung. (The circumsphere problem and linear semifinite optimization). (German) Zbl 0689.52003

Given a bounded pointset (in n-dimensional space) determine inequalities relating the radius R of the smallest ball covering A and the diameter of A. The author considers this as a linear semiinfinite optimization problem, and deduces Jungs inequality. He also considers a similar problem with the points restricted to the surface of a hemisphere. The method has application to other problems of this sort.
Reviewer: W.Moser

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A55 Spherical and hyperbolic convexity
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
49N15 Duality theory (optimization)
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