TY - INPR
A1 - SchÃ¶bel, Anita
T1 - Anchored hyperplane location problems
N2 - 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.
T3 - Report in Wirtschaftsmathematik (WIMA Report) - 74
Y1 - 2001
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1145
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-10838
ER -