A global optimization procedure for the location of a median line in the three-dimensional space |
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| Authors: | Rafael Blanquero |
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| Institution: | a Facultad de Matematicas, Universidad de Sevilla, Avda Reina Mercedes s/n, 41012 Sevilla, Spain
b Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestraße 16-18, 37083 Göttingen, Germany |
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| Abstract: | A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points.Although we are using similar techniques as for location problems in two dimensions, it is shown that the problem becomes much harder to solve. However, a problem parameterization as well as lower bounds are suggested whereby we succeeded in solving medium-size instances in a reasonable amount of computing time. |
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| Keywords: | Global optimization Geometric branch-and-bound methods Line location |
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