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

arXiv: https://arxiv.org/abs/1904.04885 · HTML: https://mlsanity.com/paper/1904.04885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization](https://mlsanity.com/paper/2609.34960/) (2026)

## Abstract (arXiv)

The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is β-Lipschitz if and only if it is 1/β-cocoercive. In this paper, we extend this theorem to Gateaux differentiable convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of C1,+ convex functions in terms of local cocoercitivity.