This arises as a part of my work.
\begin{align} \min_{x^{H}x=1}~&x^{H}A_1x \\ \text{subject to}~&x^{H}A_2x=0 \end{align}
where $A_1, A_2$ are $N \times N$ Hermitian matrices and $x$ is a unit norm complex vector to be found. Any recommendations on a iterative algorithm to solve this is also fine.