I want to solve a generalized form of a quadratic programming problem $$\min_x \left(\sqrt{x^TPx}+\sqrt{x^TQx}\right)^2+c^Tx$$, $$\textrm{ s.t. } Ax\le b.$$ Here, $P$ and $Q$ are both positive definite.
As you know, the ordinary quadratic programming only involves one positive definite matrix, i.e. $$\min_x x^TQx+c^Tx$$ $$\textrm{s.t. } Ax\le b$$
Now I want to ask how to solve the first generalized form. Thank you so much.