I have an optimization problem which is described as
$$\begin{array}{ll} \text{minimize}_x & c^{T}x\\ \text{subject to} & Gx \preceq h\\ & -x^{T}Px - qx - r \leq 0 \end{array}$$
where $P$ is positive semidefinite. Is there any way to convert this problem into a convex problem?