I'm trying to solve a problem of the form
$$\begin{array}{ll} \text{maximize} & x^H Q_0 x\\ \text{subject to} & x^H Q_i x > b_i, \quad i \in [m]\end{array}$$
where matrices $Q_0, Q_1, \dots, Q_m$ are symmetric. So this problem is an non-convex QCQP problem. I tried to solve the problem and noticed that most papers had suggested two procedures as:
Some tried to relax the problem to SDP form and then performed rank-$1$ decomposition.
Some used SDP and then branch & bound method to find the solution. To my knowledge, finding the global solution of this problem is NP-hard as BnB methods solve it.
Which method performs better? Is there any way to find the global solution in polynomial time?