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Main Title: Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
Author(s): Brandenberg, René
Theobald, Thorsten
Type: Article
Language Code: en
Abstract: We provide a characterization of the radii minimal projections of polytopes onto j-dimensional subspaces in Euclidean space . Applied to simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. In the second part of the paper, we use this characterization to determine the sequence of outer (n – 1)-radii of regular simplices (which are the radii of smallest enclosing cylinders). This settles a question which arose from an error in a paper by Weißbach (1983). In the proof, we first reduce the problem to a constrained optimization problem of symmetric polynomials and then to an optimization problem in a fixed number of variables with additional integer constraints.
Issue Date: 2006
Date Available: 10-Oct-2018
DDC Class: 510 Mathematik
Subject(s): Polytope
outer radius
regular simplex
polynomial optimization
Journal Title: Advances in Geometry
Publisher: De Gruyter
Publisher Place: Berlin
Volume: 6
Issue: 1
Publisher DOI: 10.1515/ADVGEOM.2006.005
Page Start: 71
Page End: 83
EISSN: 1615-7168
ISSN: 1615-715X
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Mathematik » Publications

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