Given the tall matrix ${\bf A} \in {\Bbb R}^{n \times m}$ (where $n > m$) and the vector ${\bf b} \in {\Bbb R}^n$,
$$ \max_{{\bf x} \in {\Bbb R}^m} \, \left\| {\bf x} \right\|_2 \quad \text{subject to} \, {\bf A} {\bf x} = {\bf b}, {\bf x} \ge {\bf 0}_m$$
I know from the construction that the constraints form a non-empty convex set, so a solution must exist. I am looking for an algorithm to find a solution to this optimization problem.