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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?

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    You can put $g(X)=C\circ (A-XB)$ where $\circ$ is the Hadamard product, and use the chain rule.2012-01-30

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