Geodesic
On a Generalized Baillon-Haddad Theorem for Convex Functions on Hilbert Space
Journal of convex analysis, Tome 22 (2015) no. 4, pp. 963-967
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The Baillon-Haddad Theorem asserts that, if the gradient operator of a convex and Fréchet differentiable function on a Hilbert space is nonexpansive, then it is firmly nonexpansive. This theorem plays an important role in iterative optimization. In this note we present a short, elementary proof of a generalization of the Baillon-Haddad Theorem.
Classification : 47H09, 90C25, 26A51, 26B25
Mots-clés : Bregman distance, convex function, firmly nonexpansive, gradient, nonexpansive, Baillon-Haddad Theorem, Krasnosel'skii-Mann Theorem 
@article{JCA_2015_22_4_JCA_2015_22_4_a3,
     author = {C. L. Byrne},
     title = {On a {Generalized} {Baillon-Haddad} {Theorem} for {Convex} {Functions} on {Hilbert} {Space}},
     journal = {Journal of convex analysis},
     pages = {963--967},
     year = {2015},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a3/}
}
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C. L. Byrne. On a Generalized Baillon-Haddad Theorem for Convex Functions on Hilbert Space. Journal of convex analysis, Tome 22 (2015) no. 4, pp. 963-967. http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a3/