
Journal of Convex Analysis 11 (2004), No. 1, 209234 Copyright Heldermann Verlag 2004 On the Regularity of the Convexification Operator on a Compact Set Rida Laraki CNRS, Lab. d'Econometrie de l'Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France, laraki@poly.polytechnique.fr Let co_{X}( . ) denote the convexification operator on bounded real functions on a convex compact set X. Several necessary and sufficient conditions for the operator co_{X}( . ) to preserve continuity and uniformly Lipschitz continuity are established. In the special case of a finite dimensional topological vector space, it is shown that (1) the preservation of continuity is equivalent to the closeness of the set of faces of X and (2) the uniform preservation of Lipschitz continuity is equivalent to X being a polytope. FullTextpdf (627 KB) for subscribers only. 