NDLI: Zero-gradient-sum algorithms for distributed convex optimization: The continuous-time case

Content Provider	IEEE Xplore Digital Library
Author	Jie Lu Choon Yik Tang
Copyright Year	2011
Description	Author affiliation: Sch. of Electr. & Comput. Eng., Univ. of Oklahoma, Norman, OK, USA (Jie Lu; Choon Yik Tang)
Abstract	This paper presents a family of continuous-time distributed algorithms called Zero-Gradient-Sum (ZGS) algorithms, which solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The ZGS algorithms are derived using a Lyapunov function candidate that exploits convexity, and get their name from the fact that they yield nonlinear networked dynamical systems whose states slide along an invariant, zero-gradient-sum manifold and converge asymptotically to the unknown minimizer. We also present a systematic way to construct ZGS algorithms, show that a subset of them converge exponentially, and obtain lower bounds on their convergence rates in terms of the convexity characteristics of the problem and the network topology, including its algebraic connectivity. Finally, we show that some of the well-studied continuous-time distributed consensus algorithms are special cases of ZGS algorithms and discuss the ramifications.
Sponsorship	Control Syst. Soc.
Starting Page	5474
Ending Page	5479
File Size	196369
Page Count	6
File Format	PDF
ISBN	9781457700804
ISSN	07431619
e-ISBN	9781457700811
DOI	10.1109/ACC.2011.5991466
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Convergence Nickel Heuristic algorithms Convex functions Trajectory Lyapunov methods Distributed algorithms
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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