Solution of a Quadratic Optimization Problem

Question

Let $\mathbf{A_1}$ and $\mathbf{A_2}$ be two given $N\times N$ hermitian matrices. Then how do I solve the problem, \begin{align} \max_{\mathbf{u}~\in~\mathbb{C}^N}~~&\mathbf{u}^H\mathbf{A_1}\mathbf{u} \\ s.t. &\mathbf{u}^H\mathbf{A_2}\mathbf{u}\geq 0 \\ &\mathbf{u}^H\mathbf{u}=1 \end{align} I already know how to solve it numerically. Note that, without the first constraint, this is the plain rayleigh-ratio.