Maximizing inner product of unit vectors

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I am working on a research project and the main algorithm is based on computing the following function:

Given a symmetric matrix $A$ and a unit vector $x_0$, compute: $\max\langle Ax,x\rangle : ||x|| = 1$ and $\langle x,x_0\rangle= 0$.

I have some bounds but neither a closed formula nor numerical solution or approximation. Any ideas will be welcomed.

Thanks