A global optimization procedure for the location of a median line in the three‐dimensional space

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.