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This paper proves that non-convex quadratically constrained quadraticprograms can be solved in polynomial time when their underlying graph isacyclic, provided the constraints satisfy a certain technical condition. Whenthis condition is not satisfied, we propose a heuristic to obtain a feasiblepoint. We demonstrate this approach on optimal power flow problems over radialnetworks.

Quadratically constrained quadratic programs on acyclic graphs with application to power flow