Let $\mathbf{A}\in\mathbb{C}^{m \times n}$ and $\mathbf{B}\in\mathbb{C}^{m \times n}$. Find the solution to the following problem:
$\min_{\mathbf{X} \in \mathbb{C}^{{m}^{2} \times r},~~ \mathbf{Y} \in \mathbb{C}^{r \times n^{2}}}~~ \|\mathbf{A} \otimes \mathbf{B}-\mathbf{X} \mathbf{Y}\|_{2}$.
It is an exercise from the matrix analysis. The formulation is very like the principal component analysis problem. But I have no idea how to handle $\otimes$ and $\mathbf{X} \mathbf{Y}$. Can anyone give any hints? Thanks very much.