I have the following problem in $x \in \mathbb C^{205}$
$$\displaystyle\min_{x}x^HAx$$
subject to the following constraints
$$x^HBx = 1$$
$$x^HC_ix = 0$$
for $i \in \{0,1,\dots,203\}$, where $A$ and $B$ are complex $205 \times 205$ matrices and can be assumed to be positive definite. The $C_i$'s are rank-$1$ matrices (each $C_i$ matrix actually only has a single row which is non-zero, namely row $i$) but there are $204$ of them and they are not definite.
I know there is likely not a single best algorithm for dealing with this type of problem, but any suggestions for things to try out would be much appreciated!