I need to find a point in the subgradient (at a certain point $x^k$) of the function $$ f(x) = \frac{1}{2}||y-Ax||^2 + ||x||_1$$ for some kind of iterative method, ie I need to find $g \in \partial f(x^k)$. Here $y$ and $A$ are constant vector and matrix chosen respectively so that the dimensions make sense.
Is there an analytic expression of a point in the subgradient of $f$ given $x^k$?
