I have this optimization problem to solve
$$\begin{array}{ll} \underset{{\bf m},x}{\text{minimize}} & \| {\bf m} \|^2 \\ \text{subject to} & {\bf h}_k^\ast {\bf m} = x_k, \quad \forall k \\ & |x_k| \ge 1, \quad \forall k\end{array}$$
where the $\bf{m}$ and $\bf{h}$ are vectors. Since $|x_k|\ge1$, so its feasible region is outside the unit circle. So my question is how do we convert this problem into a convex problem to get a solution in a much more effective and easy way?