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Eigenvalue problem with two quadratic constraints

I would like to solve the following problem: $$\begin{array}{ll} \text{minimize} & \mathbf{x}^T \mathbf{A} \mathbf{x}\\ \text{subject to} & \mathbf{x}^T\mathbf{B}\mathbf{x} = 0\\ & \mathbf{x}^T \math …