Abstract

Given a pair of convex conjugate functions ff and f∗f^*, we investigate the relationship between local Lipschitz continuity of ∇f\nabla f and local strong convexity properties of f∗f^*.

Author information

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

Ralph Tyrrell Rockafellar

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

rtr@math.washington.edu

Keywords

  • Convex functions
  • Fenchel conjugate
  • differentiability
  • Lipschitz continuity
  • local strong convexity
  • duality

References

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  2. R. T. Rockafellar, R. J.-B. Wets: Variational Analysis, Springer, Berlin (1998).https://doi.org/10.1007/978-3-642-02431-3Google Scholar
  3. A. Verona, M. E. Verona: Locally efficient monotone operators, Proc. Amer. Math. Soc. 109(1) (1990) 195–204.https://doi.org/10.1090/S0002-9939-1990-1012939-0Google Scholar

Suggested citation

R. Goebel, R. T. Rockafellar. “Local Strong Convexity and Local Lipschitz Continuity of the Gradient of Convex Functions.” Journal of Convex Analysis 15 (2008), No. 2, 263–270. https://doi.org/10.68381/jca15018

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press.