Journal of Convex Analysis 09 (2002), No. 2, 601--607
Copyright Heldermann Verlag 2002
Lipschitzian Behavior of the Fenchel Biconjugacy
Jean-Paul Penot
Dép. des Mathématiques, Université de Pau, 64000 Pau, France
jean-paul.penot@univ-pau.fr
We present sufficient conditions ensuring that the Legendre-Young-Fenchel biconjugacy is locally Lipschizian. An application to the continuity of some operations on the space of subsets of an Euclidean space is given.
Keywords: Bipolar, conjugacy, biconjugate, convex set, excess, Fenchel transform, Hausdorff distance, Minkowski difference, support function.
MSC: 26E25, 49J53; 52A20, 54C60, 52A05
[ Fulltext-pdf (240 KB)]