## Anchored hyperplane location problems

- The anchored hyperplane location problem is to locate a hyperplane passing through some given points P IR^n and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q IR^n . 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 isatmaximum 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 new results generalize known results about unrestricted hyperplane location problems.

Author: | Anita Schöbel |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-10838 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (74) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2001 |

Year of Publication: | 2001 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2001/02/08 |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |