A distributed continuous-time method for non-convex QCQPs

Xu Ma; Nicola Elia

doi:10.1016/j.sysconle.2018.09.002

A distributed continuous-time method for non-convex QCQPs

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	16-23
Number of pages	8
Journal	Systems and Control Letters
Volume	121
DOIs	https://doi.org/10.1016/j.sysconle.2018.09.002
State	Published - Nov 2018
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by the National Science Foundation, grant number CNS-1239319, USA.

Keywords

Distributed computational structure
Primal–dual optimization dynamics
QCQP
Saddle-point

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title = "A distributed continuous-time method for non-convex QCQPs",

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.",

keywords = "Distributed computational structure, Primal–dual optimization dynamics, QCQP, Saddle-point",

author = "Xu Ma and Nicola Elia",

note = "Funding Information: This research was supported by the National Science Foundation, grant number CNS-1239319, USA.",

year = "2018",

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doi = "10.1016/j.sysconle.2018.09.002",

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AU - Elia, Nicola

N1 - Funding Information: This research was supported by the National Science Foundation, grant number CNS-1239319, USA.

PY - 2018/11

Y1 - 2018/11

N2 - 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.

AB - 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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KW - Primal–dual optimization dynamics

KW - QCQP

KW - Saddle-point

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