The Chebyshev Hyperplane Optimization Problem

Authors:
G. Still;M. Streng
Affiliations:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Venue:
Journal of Global Optimization
Year:
1997

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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. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments.