I have the following function
$||{\bf A} - {\bf BC}||^2_F$,
where ${\bf A} \in \mathbb{C}^{m \times n}$, ${\bf B} \in \mathbb{C}^{m \times k}$, and ${\bf C} \in \mathbb{C}^{k \times n}$, which is a convex function w.r.t ${\bf B}$. I am looking for taylor expansion of the function w.r.t ${\bf B}$, so that I can write it in the following form:
$f(y) \geq f(x) + \nabla f(x)^H (y - x)$.
Can someone kindly suggest me how to proceed for it?