The Baillon-Haddad Theorem Revisited

@inproceedings{Bauschke2009TheBT,
  title={The Baillon-Haddad Theorem Revisited},
  author={Heinz H. Bauschke and Patrick L. Combettes},
  year={2009}
}
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. 2000 Mathematics Subject Classification: Primary 47H09, 90C25; Secondary 26A51, 26B25… CONTINUE READING