Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 557-568 (2004)
Bounds of the affine breadth eccentricity of convex bodies via semi-infinite optimization
Friedrich JuhnkeOtto-von-Guericke-Universität, Fakultät für Mathematik, PSF 4120, 39016 Magdeburg, Germany
Abstract: In this contribution we give a semi-infinite optimization approach to investigate the affine breadth eccentricity of convex bodies. An optimization-technique-based description of the minimal ellipsoid (Loewner-ellipsoid) of a convex body is used to derive an upper bound of the affine eccentricity in a very natural way. An additional special (integer programming) optimization problem shows that the obtained upper bound is the best possible one.
Keywords: Affine breadth eccentricity, minimal ellipsoid
Classification (MSC2000): 52A20, 52A40, 90C34
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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.