Lagrange multiplier for more than one constraints.

Question

How to minimize $x^TAx$ over the set $D=(x\geq 0, x^TBx=1$ and $(I-A^\dagger A)x=0$), where $A$ is copositive matrix of order $n-1$ and $B$ is strictly copositive matrix of order $n$. If I drop the last constraint from set $D$ then using Lagrange multiplier I am able to minimize $x^TAx$ over set $D$, but if I have third constraint then how to proceed? Set $D$ can be rewritten as $D=( x\in \mathbb{R}^n, x^TBx=1, h_{i}(x)=0, 1\leq i\leq n$) where $h_{i}(x)=\langle (I-A^\dagger A)e^{i},x \rangle=0$