I'm trying to expand this Frobenius form $||C \circ (A-XB)||_F^2$ (here $\circ$ is the Hadamard point-wise multiplication). I want to find the minimum value with respect to X.
$ \frac{\partial}{\partial X}||C \circ (A-XB)||_F^2 = 0$
I've being trying to develop using the fact that the Frobenius form is $||A||_F^2=trace(AA^*)$ but the Hadamard product is always on my way.
How would you approach this?