Let $\mathbf{A_1}$ and $\mathbf{A_2}$ be two hermitian matrices. Consider the problem
\begin{align}
\max_{\mathbf{u}^H\mathbf{u}=1}~\mathbf{u}^H\mathbf{A}_1\mathbf{u} \\\
\mathbf{u}^H\mathbf{A}_2\mathbf{u}\geq 0
\end{align} 
I know how to numerically solve it, for example Semi-Definite Relaxation is easily applicable. I was wondering if there is an analytic approach to it. Note that without the constraint, this is equivalent to the maximum rayleigh-ritz ratio.