A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 114-120
Received: May 25, 2016; Accepted: Jun. 7, 2016; Published: Jun. 18, 2016
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Authors
Ping Liu, College of Electronic and Information Engineering, Southwest University, Chongqing, PR China
Huaqing Li, College of Electronic and Information Engineering, Southwest University, Chongqing, PR China; State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, PR China
Liping Feng, Department of Computer Science and Technology of Xinzhou Normal University, Xinzhou, Shanxi, PR China
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Abstract
This paper considers a second-order multi-agent system for solving the non-smooth convex optimization problem, where the global objective function is a sum of local convex objective functions within different bound constraints over undirected graphs. A novel distributed continuous-time optimization algorithm is designed, where each agent only has an access to its own objective function and bound constraint. All the agents cooperatively minimize the global objective function under some mild conditions. In virtue of the KKT condition and the Lagrange multiplier method, the convergence of the resultant dynamical system is ensured by involving the Lyapunov stability theory and the hybrid LaSalle invariance principle of differential inclusion. A numerical example is conducted to verify the theoretical results.
Keywords
Distributed Optimization, Multi-Agent Network, Lyapunov Method, Bound Constraint, Continuous-Time
To cite this article
Ping Liu, Huaqing Li, Liping Feng, A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 114-120. doi: 10.11648/j.acm.20160503.14
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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