caa a22 4500 469075244 CHVBK 20180323132933.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF02187841 doi (NATIONALLICENCE)springer-10.1007/BF02187841 Inner and outer j -radii of convex bodies in finite-dimensional normed spaces [Elektronische Daten] [Peter Gritzmann, Victor Klee] This paper is concerned with the various inner and outer radii of a convex bodyC in ad-dimensional normed space. The innerj-radiusr j (C) is the radius of a largestj-ball contained inC, and the outerj-radiusR j (C) measures how wellC can be approximated, in a minimax sense, by a (d —j)-flat. In particular,r d (C) andR d (C) are the usual inradius and circumradius ofC, while 2r 1(C) and 2R 1(C) areC's diameter and width. Motivation for the computation of polytope radii has arisen from problems in computer science and mathematical programming. The radii of polytopes are studied in [GK1] and [GK2] from the viewpoint of the theory of computational complexity. This present paper establishes the basic geometric and algebraic properties of radii that are needed in that study. Springer-Verlag New York Inc., 1992 Gritzmann Peter Universität Trier, FBIV, Mathematik, Postfach 3825, W-5500, Trier, Federal Republic of Germany aut Klee Victor Department of Mathematics, University of Washington, 98195, Seattle, WA, USA aut Discrete & Computational Geometry Springer New York 7/3(1992-03-01), 255-280 0179-5376 7:3<255 1992 7 454 https://doi.org/10.1007/BF02187841 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02187841 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gritzmann Peter Universität Trier, FBIV, Mathematik, Postfach 3825, W-5500, Trier, Federal Republic of Germany aut NATIONALLICENCE 700 1- Klee Victor Department of Mathematics, University of Washington, 98195, Seattle, WA, USA aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 7/3(1992-03-01), 255-280 0179-5376 7:3<255 1992 7 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer