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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.

Ralph Tyrell Rockafellar
Dept. of Mathematics, University of Washington, Seattle, WA 98195-4350, U.S.A.


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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