The Baillon-Haddad Theorem Revisited

Heinz H. Bauschke; Patrick L. Combettes

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arXiv · 0906.0807

The Baillon-Haddad Theorem Revisited

Heinz H. Bauschke·Patrick L. Combettes

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Abstract

In 1977, Baillon and Haddad proved that if the gradient of a convex and continuously differentiable function is nonexpansive, then it is actually firmly nonexpansive. This result, which has become known as the Baillon-Haddad theorem, has found many applications in optimization and numerical functional analysis. In this note, we propose short alternative proofs of this result and strengthen its conclusion.

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Heinz H. Bauschke, Patrick L. Combettes. 2009-12-22. The Baillon-Haddad Theorem Revisited. https://arxiv.org/abs/0906.0807

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