Abstract
We consider the following problem. Given a finite set of pointsy^j inR^n we want to determine a hyperplaneH such that the maximum Euclidean distance betweenH and the pointsy^j is minimized. This problem (CHOP) is a non-convex optimization problem with a special structure. For example, all local minima can be shown to be strongly unique. We present a genericity analysis of the problem. Two different global optimization approaches are considered for solving (CHOP). The first is a Lipschitz optimization method; the other a cutting plane method for concave optimization. The local structure of the problem is elucidated by analysing the relation between (CHOP) and certain associated linear optimization problems. We report on numerical experiments.
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