I need to solving following quadratic fractional programming problem: \begin{equation} \begin{matrix} \min_w \frac{w^\top Q w}{w^\top (r r^\top) w} \\ \text{s.t.}\quad w\geq 0 \\ \sum w =1 \end{matrix} \end{equation} where $w\in\Re^{n,1}$, $Q$ is a given positive definite matrix and $r\in\Re^{n,1}$ is a given vector.
This is my first time solving this kind of problems, do I have do some change of variables first? (https://en.wikipedia.org/wiki/Fractional_programming), i.e. \begin{equation} t=\frac{1}{r^\top w}, \qquad y=tw \end{equation} then the original problem becomes \begin{equation} \begin{matrix} \min_y y^\top Q y \\ \text{s.t.}\quad y\geq 0 \\ \sum y = t\\ r^\top y =1 \end{matrix} \end{equation}
which solver could I use?
Many thanks