Consider the following optimization problem;
$\min_{M} ~\|a-M*b\|_2$
subject to
$\|M\|_2<1$.
where $M\in R^{5\times3}$ and a and b are constant vectors.
There might be many optimal solutions to the problem above. I'm wondering if there's a theory/method to get the set of matrices M such that they all minimize the problem above.