Reducing trace minimization to generalized eigenvalue problem

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I'm looking for insight in solving the following optimization over symmetric matrices A and positive-definite H.

$$R=\max_{A}\frac{\text{tr}(HA)^2+2\text{tr}(HAHA)}{\text{tr}(AHA)}$$

The paper originally states that this reduces to generalized eigenvalue problem, can anyone see the conversion?

Using CAS I can see the following sample solution

$$R=\frac{9+\sqrt{17}}{2}$$ for $$H=\left(\begin{matrix} 1 & 0 \\ 0 & 2\end{matrix}\right)$$