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.
Bibliographical noteFunding Information:
This research was supported by the National Science Foundation, grant number CNS-1239319, USA.
- Distributed computational structure
- Primal–dual optimization dynamics