Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
| dc.contributor.author | Brandenberg, René | |
| dc.contributor.author | Theobald, Thorsten | |
| dc.date.accessioned | 2018-10-10T07:34:44Z | |
| dc.date.available | 2018-10-10T07:34:44Z | |
| dc.date.issued | 2006 | |
| dc.description | Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich. | de |
| dc.description | 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. | en |
| dc.description.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. | en |
| dc.identifier.eissn | 1615-7168 | |
| dc.identifier.issn | 1615-715X | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/8313 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-7464 | |
| dc.language.iso | en | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | Polytope | en |
| dc.subject.other | Projection | en |
| dc.subject.other | outer radius | en |
| dc.subject.other | regular simplex | en |
| dc.subject.other | polynomial optimization | en |
| dc.title | Radii minimal projections of polytopes and constrained optimization of symmetric polynomials | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1515/ADVGEOM.2006.005 | |
| dcterms.bibliographicCitation.issue | 1 | |
| dcterms.bibliographicCitation.journaltitle | Advances in Geometry | en |
| dcterms.bibliographicCitation.originalpublishername | De Gruyter | en |
| dcterms.bibliographicCitation.originalpublisherplace | Berlin | en |
| dcterms.bibliographicCitation.pageend | 83 | |
| dcterms.bibliographicCitation.pagestart | 71 | |
| dcterms.bibliographicCitation.volume | 6 | |
| tub.accessrights.dnb | domain | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | de |
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