I am reviewing a paper in which the solution to $$x =\max_\bf{v}\frac{\alpha \bf{v}^\dagger \bf{h}\bf{h}^\dagger \bf{v}}{\beta+\gamma\bf{v}^\dagger \bf{D} \bf{v}},\;\mathrm{such\;that\;\bf{v}^\dagger(\gamma\bf{I}+\alpha \hat{\bf{D}})\bf{v} <\delta}$$ is said to be $$x= \alpha \bf{h}^\dagger\left(\frac{\beta(\gamma \bf{I}+\alpha\hat{\bf{D}})}{\delta}+ \gamma{\bf{D}}\right)^{-1} \bf{h}, $$ where $\alpha,\beta,\gamma,\delta$ are positive scalars, $\bf{I}$ is an appropriately dimensioned identity matrix, $\bf v$ and $\bf h$ are complex column vectors and $\bf{D},\hat{\bf{D}}$ are real diagonal matrices.
It is claimed that the problem is a generalized eigenvector problem. I've been scouring the internet for a similar example that I can correlate with this one, but haven't had any luck. Could anyone explain how this solution is obtained?