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Bounds of the affine breadth eccentricity of convex bodies via semi-infinite optimization

by Juhnke, F..

Series: 2003-42, Preprints

52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)
52A40 Inequalities and extremum problems
90C34 Semi-infinite programming

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.

Affine breadth eccentricity, minimal ellipsoid

This paper was published in:
Beitraege zur Algebra und Geometrie / Contributions to algebra and geometry