Juhnke, Friedrich Das Umkugelproblem und lineare semiinfinite Optimierung. (The circumsphere problem and linear semifinite optimization). (German) Zbl 0689.52003 Beitr. Algebra Geom. 28, 147-156 (1989). 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 Cited in 1 Document 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) Keywords:ball covering; linear semiinfinite optimization; Jungs inequality PDFBibTeX XMLCite \textit{F. Juhnke}, Beitr. Algebra Geom. 28, 147--156 (1989; Zbl 0689.52003) Full Text: EuDML