The Baillon-Haddad Theorem Revisited
Optimization and Control
2009-12-22 v2 Functional Analysis
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.
Cite
@article{arxiv.0906.0807,
title = {The Baillon-Haddad Theorem Revisited},
author = {Heinz H. Bauschke and Patrick L. Combettes},
journal= {arXiv preprint arXiv:0906.0807},
year = {2009}
}