Subdifferential
= Subdifferential
{title2=$\partial f(x)$}
{wiki}
For a convex function $f$, the subdifferential at $x$ is
$$
\partial f(x)=\{g:f(y)\geq f(x)+g^T(y-x)\text{ for every }y\}.
$$
The point $x$ minimizes $f$ exactly when $0\in\partial f(x)$.