Journal of Convex Analysis 15 (2008), No. 2, 263--270
Copyright Heldermann Verlag 2008
Local Strong Convexity and Local Lipschitz Continuity of the Gradient of Convex Functions
Rafal Goebel
3518 NE 42 Street, Seattle, WA 98105, U.S.A.
rafal.k.goebel@gmail.com
Ralph Tyrell Rockafellar
Dept. of Mathematics, University of Washington, Seattle, WA 98195-4350, U.S.A.
rtr@math.washington.edu
[Abstract-pdf]
Given a pair of convex conjugate functions $f$ and $f^*$, we investigate the relationship between local Lipschitz continuity of $\nabla f$ and local strong convexity properties of $f^*$.
Keywords: Convex functions, Fenchel conjugate, differentiability, Lipschitz continuity, local strong convexity, duality.
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