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), 2016. Published by Science Publishing Group

Keywords

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

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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

Copy | Download

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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