Abstract

Let coX(⋅)co_X(\cdot) denote the convexification operator on bounded real functions on a convex compact set X. Several necessary and sufficient conditions for the operator coX(⋅)co_X(\cdot) 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

Author information

Contact details are reproduced from the original publication and may be historical.

Rida Laraki

CNRS, Lab. d'Econométrie de l'Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France
and: Modal’X (Université Paris-10 Nanterre)
and: Ceremade (Université Paris-9 Dauphine)

laraki@poly.polytechnique.fr

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Suggested citation

R. Laraki. “On the Regularity of the Convexification Operator on a Compact Set.” Journal of Convex Analysis 11 (2004), No. 1, 209–234. https://doi.org/10.68381/jca11014

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.