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2003-42

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

by Juhnke, F..


Series: 2003-42, Preprints

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

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

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