Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
| dc.creator | Brandenberg, Rene | |
| dc.creator | Theobald, Thorsten | |
| dc.date | 2003-11-03 | |
| dc.date | 2005-10-11 | |
| dc.date.accessioned | 2026-07-07T06:35:47Z | |
| dc.date.available | 2026-07-07T06:35:47Z | |
| dc.description | We provide a characterization of the radii minimal projections of polytopes onto $j$-dimensional subspaces in Euclidean space $\E^n$. Applied on 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 the incidence that a paper by Weißbach (1983) on this determination was erroneous. 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. | |
| dc.description | Minor revisions. To appear in Advances in Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0311017 | |
| dc.identifier | http://arxiv.org/abs/math/0311017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99898 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 51N20; 52A15; 52B12; 52B55; 68W30 | |
| dc.title | Radii minimal projections of polytopes and constrained optimization of symmetric polynomials | |
| dc.type | text |