An algorithm for finding the Chebyshev center of a convex polyhedron

An algorithm for finding the Chebyshev center of a finite point set in the Euclidean spaceRⁿ is proposed. The algorithm terminates after a finite number of iterations. In each iteration of the algorithm the current point is projected orthogonally onto the convex hull of a subset of the given point set.Part of this research was done at the University of Würzburg (Institut für Angewandte Mathematik und Statistik) when the first author was supported by the Alexander von Humboldt Foundation, Germany.On leave from the Institute of Mathematics and Mechanics, Ural Department of Russia Academy of Sciences, 620219 Ekaterinburg, S. Kovalevskaya str.16, Russia.