I am trying to solve following problem: \begin{equation} \begin{aligned} \min_{x\in\Re^{n\times1}} &\frac{x^\top H x + f^\top x + C_e}{\sqrt{x^\top R x + C_v}}\\ \text{s.t.} &~~Ax\leq b \end{aligned} \end{equation} where $H$ and $R$ are both positive semidefinite matrics. both $C_e$ and $C_v$ are positive scalar.
I know that if there is NO "square root" in denominator, we could let $z^2=\frac{1}{x^\top R x + C_v}$ and $x=y/z$, then the quadratic fractional problem can be transferred into a non-convex QCQP problem about $z$ and $y$.
Does anyone know how to deal with "square root of quadratic funcion" in denominator? Many thanks!!