Subgradient optimality condition
= Subgradient optimality condition
{title2=$0\in\partial f(x)$}
A proper convex function $f$ is minimized at $x$ exactly when $0\in\partial f(x)$. For a differentiable convex term $g$ and another convex term $h$, the <subdifferential sum rule> gives the condition $0\in\nabla g(x)+\partial h(x)$.