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Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
Brandenberg, René; Theobald, Thorsten
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.
- 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.
