A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization

Ping Liu; Huaqing Li; Liping Feng

doi:doi:10.11648/j.acm.20160503.14

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A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization

Ping Liu, Huaqing Li, Liping Feng

Published in Applied and Computational Mathematics (Volume 5, Issue 3)

Received: 25 May 2016 Accepted: 7 June 2016 Published: 18 June 2016

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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.

Published in	Applied and Computational Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.acm.20160503.14
Page(s)	114-120
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Distributed Optimization, Multi-Agent Network, Lyapunov Method, Bound Constraint, Continuous-Time

References

[1]	Han D, Mo Y, Wu J, et al. Stochastic event-triggered sensor schedule for remote state estimation. IEEE Transactions on Automatic Control, 2015, 60(10): 2661-2675.
[2]	Li H, Liao X, Huang T, et al. Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Transactions on Automatic Control, 2015, 60(7): 1998-2003.
[3]	Olfati-Saber R, Fax A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 2007, 95(1): 215-233.
[4]	Xia Z, Wang X, Sun X, et al. Steganalysis of least significant bit matching using multi-order differences. Security and Communication Networks, 2014, 7(8): 1283-1291.
[5]	Lobel I, Ozdaglar A. Distributed subgradient methods for convex optimization over random networks. IEEE Transactions on Automatic Control, 2011, 56(6): 1291-1306.
[6]	Guo P, Wang J, Geng X H, et al. A variable threshold-value authentication architecture for wireless mesh networks. Journal of Internet Technology, 2014, 15(6): 929-935.
[7]	Nedić A, Ozdaglar A, Parrilo P A. Constrained consensus and optimization in multi-agent networks. IEEE Transactions on Automatic Control, 2010, 55(4): 922-938.
[8]	Ren W, Beard R W. Distributed consensus in multi-vehicle cooperative control. Springer-Verlag, London, 2008.
[9]	Li H, Chen G, Liao X, et al. Quantized data-based leader-following consensus of general discrete-time multi-agent systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 2016, 63(4): 401-405.
[10]	Wang J, Elia N. Control approach to distributed optimization. Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on. IEEE, 2010: 557-561.
[11]	Gharesifard B, Cortés J. Distributed continuous-time convex optimization on weight-balanced digraphs. IEEE Transactions on Automatic Control, 2014, 59(3): 781-786.
[12]	Liu S, Qiu Z, Xie L. Continuous-time distributed convex optimization with set constraints. Proceedings of the 19th IFAC World Congress, Cape Town, South Africa. 2014: 9762-9767.
[13]	Li H, Liao X, Huang T, et al. Second-order global consensus in multi-agent networks with random directional link failure. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(3): 565-575.
[14]	Gungor V C, Hancke G P. Industrial wireless sensor networks: Challenges, design principles, and technical approaches. IEEE Transactions on Industrial Electronics, 2009, 56(10): 4258-4265.
[15]	Shen J, Tan H W, Wang J, et al. A novel routing protocol providing good transmission reliability in underwater sensor networks. Journal of Internet Technology, 2015, 16(1): 171-178. 2015, 16(1): 171-178.
[16]	Li H, Chen G, Huang T, et al. High-performance consensus control in networked systems with limited bandwidth communication and time-varying directed topologies. IEEE Transactions on Neural Networks and Learning Systems, 2016, DOI: 10.1109/TNNLS.2016.2519894.
[17]	Blatt D, Hero III A O. Energy-based sensor network source localization via projection onto convex sets. IEEE Transactions on Signal Processing, 2006, 54(9): 3614-3619.
[18]	Wen X, Shao L, Xue Y, et al. A rapid learning algorithm for vehicle classification. Information Sciences, 2015, 295: 395-406.
[19]	Yi P, Hong Y, Liu F. Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and its application to economic dispatch of power systems. arXiv preprint arXiv:1510.08579, 2015.
[20]	Li H, Liao X, Chen G, et al. Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Networks, 2015, 66: 1-10.
[21]	Gu B, Sheng V S, Tay K Y, et al. Incremental support vector learning for ordinal regression. IEEE Transactions on Neural networks and learning systems, 2015, 26(7): 1403-1416.
[22]	Wen G, Duan Z, Chen G, et al. Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies. IEEE Transactions on Circuits and Systems I: Regular Papers, 2014, 61(2): 499-511.
[23]	Xie S, Wang Y. Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wireless personal communications, 2014, 78(1): 231-246.
[24]	Zhu M, Martínez S. On distributed convex optimization under inequality and equality constraints. IEEE Transactions on Automatic Control, 2012, 57(1): 151-164.
[25]	Nedić A, Ozdaglar A. Distributed subgradient methods for multi-agent optimization. IEEE Transactions on Automatic Control, 2009, 54(1): 48-61.
[26]	Bianchi P, Jakubowicz J. Convergence of a multi-agent projected stochastic gradient algorithm for non-convex optimization. IEEE Transactions on Automatic Control, 2013, 58(2): 391-405.
[27]	Lou Y, Shi G, Johansson K H, et al. Approximate projected consensus for convex intersection computation: Convergence analysis and critical error angle. IEEE Transactions on Automatic Control, 2014, 59(7): 1722-1736.
[28]	Zhu M, Martinez S. On distributed convex optimization under inequality and equality constraints via primal-dual subgradient methods. arXiv preprint arXiv:1001.2612, 2010.
[29]	Yuan D, Xu S, Zhao H. Distributed primal–dual subgradient method for multiagent optimization via consensus algorithms. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2011, 41(6): 1715-1724.
[30]	Li H, Chen G, Huang T, et al. Event-triggered distributed average consensus over directed digital networks with limited communication bandwidth. IEEE Transactions on Cybernetics, 2016, DOI: 10.1109/TCYB.2015.2496977.
[31]	Ruszczyński A P. Nonlinear Optimization. Princeton university press, 2006.

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APA Style

Ping Liu, Huaqing Li, Liping Feng. (2016). A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Applied and Computational Mathematics, 5(3), 114-120. https://doi.org/10.11648/j.acm.20160503.14

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ACS Style

Ping Liu; Huaqing Li; Liping Feng. A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Appl. Comput. Math. 2016, 5(3), 114-120. doi: 10.11648/j.acm.20160503.14

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AMA Style

Ping Liu, Huaqing Li, Liping Feng. A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Appl Comput Math. 2016;5(3):114-120. doi: 10.11648/j.acm.20160503.14

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@article{10.11648/j.acm.20160503.14,
  author = {Ping Liu and Huaqing Li and Liping Feng},
  title = {A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {3},
  pages = {114-120},
  doi = {10.11648/j.acm.20160503.14},
  url = {https://doi.org/10.11648/j.acm.20160503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.14},
  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.},
 year = {2016}
}

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TY  - JOUR
T1  - A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization
AU  - Ping Liu
AU  - Huaqing Li
AU  - Liping Feng
Y1  - 2016/06/18
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.14
DO  - 10.11648/j.acm.20160503.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 114
EP  - 120
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.14
AB  - 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.
VL  - 5
IS  - 3
ER  -

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Author Information

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
Liping Feng

Department of Computer Science and Technology of Xinzhou Normal University, Xinzhou, Shanxi, PR China

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APA Style

Ping Liu, Huaqing Li, Liping Feng. (2016). A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Applied and Computational Mathematics, 5(3), 114-120. https://doi.org/10.11648/j.acm.20160503.14

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ACS Style

Ping Liu; Huaqing Li; Liping Feng. A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Appl. Comput. Math. 2016, 5(3), 114-120. doi: 10.11648/j.acm.20160503.14

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AMA Style

Ping Liu, Huaqing Li, Liping Feng. A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization. Appl Comput Math. 2016;5(3):114-120. doi: 10.11648/j.acm.20160503.14

Copy | Download

@article{10.11648/j.acm.20160503.14,
  author = {Ping Liu and Huaqing Li and Liping Feng},
  title = {A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {3},
  pages = {114-120},
  doi = {10.11648/j.acm.20160503.14},
  url = {https://doi.org/10.11648/j.acm.20160503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.14},
  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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization
AU  - Ping Liu
AU  - Huaqing Li
AU  - Liping Feng
Y1  - 2016/06/18
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.14
DO  - 10.11648/j.acm.20160503.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 114
EP  - 120
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.14
AB  - 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.
VL  - 5
IS  - 3
ER  -

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