Derivative of the nuclear norm The nuclear norm is defined in the following way
$$\|X\|_*=\mathrm{tr} \left(\sqrt{X^T X} \right)$$
I'm trying to take the derivative of the nuclear norm with respect to its argument
$$\frac{\partial \|X\|_*}{\partial X}$$
Note that $\|X\|_*$ is a norm and is convex. I'm using this for some coordinate descent optimization algorithm. Thank you for your help.

What about $|| M ||_{F} = \mathrm{Trace}(M^{T}M)$?
