Duality between Fréchet differentiability and strong convexity

Duality between Fréchet differentiability and strong convexity This paper revisits the duality between differentiability and strict or strong convexity under the Legendre–Fenchel transform $${f\mapsto f^*}$$ . Functions f defined on a Banach space X are considered. For a lower semicontinuous but not necessarily convex function f we relate essential Fréchet differentiability of the conjugate function f* to essential strong convexity of f. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Duality between Fréchet differentiability and strong convexity

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0105-5
Publisher site
See Article on Publisher Site

Abstract

This paper revisits the duality between differentiability and strict or strong convexity under the Legendre–Fenchel transform $${f\mapsto f^*}$$ . Functions f defined on a Banach space X are considered. For a lower semicontinuous but not necessarily convex function f we relate essential Fréchet differentiability of the conjugate function f* to essential strong convexity of f.

Journal

PositivitySpringer Journals

Published: Dec 4, 2010

References

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