Baillon–Haddad theorem
= Baillon–Haddad theorem
{c}
{title2=$\langle\nabla f(u)-\nabla f(v),u-v\rangle\geq L^{-1}\|\nabla f(u)-\nabla f(v)\|^2$}
On the whole Euclidean space, an $L$-<Lipschitz gradient> of a <convex function> is $1/L$-cocoercive. Subtract the supporting affine function at one point, apply the <descent lemma> to a gradient step at the other point, then interchange the points and add. The conclusion needs convexity but no second derivative.