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A quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions.
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Solving a non-convex quadratically-constrained quadratic program
Your non-convex constraint is that $x$ lies on the outside of the intersection of some set of ellipsoids, which is a convex region $S$. You can try to randomly sample the surface of this set for rando …