Abstract

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.

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Keywords

  • Bipolar
  • conjugacy
  • biconjugate
  • convex set
  • excess
  • Fenchel transform
  • Hausdorff distance
  • Minkowski difference
  • support function

Mathematics Subject Classification

26E25, 49J53; 52A20, 54C60, 52A05

Suggested citation

J.-P. Penot. “Lipschitzian Behavior of the Fenchel Biconjugacy.” Journal of Convex Analysis 9 (2002), No. 2, 601–607.

Copyright Heldermann Verlag 2002