Consider the $p\to q$ norm for a matrix $A \in \mathbb{R}^{m\times n}$ where
$$ \|A\|_{p\to q} = \max_{x \in \mathbb{R}^n \setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p} $$
(defined as in https://arxiv.org/abs/1802.07425)
I'm interested in the special case when $p = 2$ and $q=1$. Is the subgradient of the function $f(A) = \|A\|_{2\to 1}$ known?