03-42
Bounds of the affine breadth eccentricity of convex bodies via semi-infinite optimization
by Juhnke, F.
Preprint series: 03-42, Preprints
The paper is published: Beitraege zur Algebra und Geometrie / Contributions to algebra and geometry
- MSC:
- 52A20 Convex sets in $n$ dimensions (including convex hypersurfaces), See also {53A07, 53C45}
- 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
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