About factorization with respect to tensor product.

Question

So I was trying to factorize some tensor $w_{mn}$ into $v_m \otimes u_n$. But such factorization does not always exist. Therefore I turned into an estimate problem:
Given complex valued $A_{m\times n}$, how can we find $u_{m\times 1}, v_{n\times 1}$ that minimize $\|A-u\otimes v\| = \|A-u^Tv\|$?
In which the norm chosen can be arbitrary, for example, l2 norm (square variance).
What I really need is some sort of numerical algorithm that is efficient enough. But I just cannot think of any easy way to solve it.