Partial subdifferential
= Partial subdifferential
{title2=$\partial_y f(x,y)$}
For a convex scalar function $f(x,y)$, the partial subdifferential $\partial_y f(x,y)$ means the <subdifferential> of $v\mapsto f(x,v)$ at $v=y$. It is not differentiation of a set-valued subdifferential. If this section is differentiable, the partial subdifferential is the singleton containing $\nabla_yf(x,y)$.