I am looking for a reference for an algorithm to solve the following type of optimization problem:
$$\begin{aligned}\text{Minimize } & x^TQx \text{ where } Q \text{ is symmetric and positive definite}\\ &\text{subject to: } Ax\leq b \text{ and}\\ &x^TB_ix=k_i^2 \text{ for }i\in I \text{ and }B_i \text{ symmetric and positive semi-definite} \end{aligned}$$
I know how to do both linear and quadratic programming with linear equality and inequality constraints, but quadratic equality constraints are nonconvex, so these methods won't work without some adaptation.
I came across this optimization problem while studying the question of constructing a polyhedral lift of a planar embedding of a graph. It turns out that setting a facet normal is a linear condition in the variables I am using, but setting the facet's angle above the $xy$-plane without specifying its azimuth gives rise to a quadratic equality constraint.
If someone can recommend a good textbook where this type of situation is covered, or even some keywords for me to research, I would be grateful.