Consider the following optimization problem
$$\min \qquad \omega^H \omega \\ \text{s. t.} \quad \omega^H A \omega \geq a, \\ \quad \quad \omega^H B \omega \geq b $$
where $A$ and $B$ are $m \times m$ postive semi-definite matrices, $\omega$ is $m \times 1$ vector and $a$ and $b$ are scalars. Does this optimization problem have a closed form solution? If so, please give me link or explanation.
I look forward to your priceless answer. Thank you!
ps)edit: semi-definite matrices -> positive semi-definite matrices