The Baillon-Haddad Theorem Revisited

Details The Baillon-Haddad Theorem Revisited The Baillon-Haddad Theorem Revisited

2009-06-04

arxiv.org/abs/0906.0807v2

Mathematics

Optimization and Control

Scientific paper

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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