I have the following problem.
Let $A$, $B$ $C$ be real-valued matrices of size $m \times q$, $m \times n$, $p \times q$ respectively. Find matrix $X$ of size $n \times p$ and maximum rank $r$ such that the Frobenius norm $\|A - B X C \|$ is minimized.
This is a generalization of the best approximation property of the truncated Singular Value Decomposition; however it doesn't appear to be trivial. Any insights? Known literature?