Let $A$ be an $m\times n$ matrix with entries in $F$ ($F=\mathbb{R}$ or $F=\mathbb{C}$). 
It is well-known that $A$ has decompositions of the form 
$$\displaystyle A = \sum_{k=1}^r\lambda_k\hspace{2mm} x_k\otimes y_k$$
for some $r\in\mathbb{N}$ and $\lambda_k>0$, $x_k\in F^m$, $y_k\in F^n$, for example via SVD.
Consider the problem
$$\begin{array}{rl}
\min & \sum_{k=1}^r \lambda_k \\
\textrm{subject to }1: & A = \sum_{k=1}^r \lambda_k \hspace{2mm} x_k\otimes y_k \\
2: & \lambda_k>0 \\
3: & -1\leq x_k \leq 1, \hspace{2mm} -1\leq y_k\leq 1 \hspace{15mm} (\textrm{if}\hspace{2mm}F=\mathbb{R})\\
3':& |x_k| \leq 1, \hspace{2mm} |y_k|\leq 1 \hspace{15mm} (\textrm{if}\hspace{2mm}F=\mathbb{C})\\
\end{array}$$
Here $r$ can vary from one decomposition to another.
It can be shown the solutions exist by a compactness argument.

**Question:** How can we algorithmically calculate a decomposition of $A$, which solves the minimization problem above? What's the speed of known (if any) algorithms as $m,n\to\infty$?