A Quadratically-Constrainted Quadratic Program consists of optimizing a quadratic objective function while imposing quadratic constraints, which can be inequalities or equalities. Obviously, describing the problem with inequalities alone can suffice, as $a\le b$ and $a\ge b$ is equivalent to just $a=b$. For this reason, a lot of literature just focuses on the inequalities.
However, I only have quadratic equality constraints, without any inequalities. In fact, it's enough constraints, that I believe in my case the space of points satisfying the constraints is discrete (like $2^{n/2}$ separate points or something). So it becomes very little of an "optimization" problem, and much more of a "search space" problem. I would like to figure out a way to transform this system into a form amenable to discrete search, but I can't find any directives on how to accomplish that. All the heuristics/approximations I could find for QCQP definitely seem to treat more of the "not very constrained" case, where you're moving around continuously in the allowed region -- that picture doesn't apply here, though.
I realize that searching all $2^{n/2}$ points is intractable in general, of course. But I hope that whatever form it would come in would then be amenable to its own heuristic searches, like a binary quadratic program is.
