Let $$f(K) = \| K \|_*$$ be the nuclear norm (sum of the singular values) of $K=U\Sigma V^T$. How can one compute the subdifferential $\partial f$?
This may be a basic question, I'm trying to work my way through a paper in which minimizing $f$ over a convex set of matrices plays a central role. For what it's worth, I have found papers that display the end result, but not the derivation.
EDIT: This paper by Tao and Candes derives an expression, but refers the proof to "Characterization of the subdifferential of some matrix norms" which does not prove it as far as I can tell. I also found a class homework assignment posted online that said this was easy to "grind out" with matrix derivatives, but that there was another way via projections. Any guidance would be greatly appreciated.