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Radii minimal projections of polytopes and constrained optimization of symmetric polynomials

Radii minimal projections of polytopes and constrained optimization of symmetric polynomials 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Radii minimal projections of polytopes and constrained optimization of symmetric polynomials

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Publisher
de Gruyter
Copyright
Copyright © 2006 by the
ISSN
1615-715X
eISSN
1615-7168
DOI
10.1515/ADVGEOM.2006.005
Publisher site
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Abstract

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.

Journal

Advances in Geometry – de Gruyter

Published: Jan 26, 2006

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