## Anchored Hyperplane Location Problems

 dc.contributor.author Schöbel, Anita dc.date.accessioned 2010-11-16T08:02:48Z dc.date.available 2010-11-16T08:02:48Z dc.date.issued 2003 dc.identifier.citation Schöbel, Anita (2003): Anchored Hyperplane Location Problems - Discrete and Computational Geometry, Vol. 29, Nr. 2, p. 229-238 dc.identifier.uri http://resolver.sub.uni-goettingen.de/purl?gs-1/5712 dc.description.abstract The anchored hyperplane location problem is to locate a hyperplane passing through some given points P ⊆ Rn and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q ⊆ Rn . This problem of computational geometry is analyzed by using nonlinear programming techniques. If the distances are measured by a norm, it will be shown that in the median case there exists an optimal hyperplane that passes through at least n − k affinely independent points of Q, if k is the maximum number of affinely independent points of P. In the center case, there exists an optimal hyperplane which is at maximum distance to at least n −k +1 affinely independent points of Q. Furthermore, if the norm is a smooth norm, all optimal hyperplanes satisfy these criteria. These results generalize known results about unrestricted hyperplane location problems. dc.language.iso eng dc.rights openAccess dc.subject Hyperplane Location Problems dc.subject.ddc 510 dc.title Anchored Hyperplane Location Problems dc.type journalArticle dc.identifier.doi 10.1007/s00454-002-0741-z dc.type.version submittedVersion dc.bibliographicCitation.volume 29 dc.bibliographicCitation.issue 2 dc.bibliographicCitation.firstPage 229 dc.bibliographicCitation.lastPage 238 dc.type.subtype journalArticle dc.description.status peerReviewed dc.bibliographicCitation.journal Discrete and Computational Geometry
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