Abstract
This paper studies non-convex Quadratically Constrained Quadratic Programmings (QCQPs) via the continuous-time optimization dynamics. We first develop an easily checkable necessary and sufficient condition that characterizes whether a KKT point will also be a saddle-point (the pair of primal and dual optima) for a non-convex QCQP. Then we analyze the semistability of the saddle-point equilibrium set with respect to the proposed optimization dynamics. We also point out that, for certain networked QCQPs, the proposed approach exhibits an intrinsic distributed computational structure.
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