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arXiv · 1904.04885

An enhanced Baillon-Haddad theorem for convex functions on convex sets

Pedro Pérez-Aros·Emilio Vilches
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Abstract

The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is $\beta$-Lipschitz if and only if it is $1/\beta$-cocoercive. In this paper, we extend this theorem to G\^{a}teaux differentiable convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of $C^{1,+}$ convex functions in terms of local cocoercitivity.

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Pedro Pérez-Aros, Emilio Vilches. 2019-04-09. An enhanced Baillon-Haddad theorem for convex functions on convex sets. https://arxiv.org/abs/1904.04885

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