Distributed Primal-Dual Subgradient Method for Multiagent Optimization via Consensus Algorithms

This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the L...

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Veröffentlicht in:	IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Jg. 41; H. 6; S. 1715 - 1724
Hauptverfasser:	Deming Yuan, Shengyuan Xu, Huanyu Zhao
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States IEEE 01.12.2011
Schlagworte:	Algorithm design and analysis Approximation algorithms Average consensus Convergence Convex functions convex optimization distributed optimization Lagrangian functions Optimization subgradient method Upper bound
ISSN:	1083-4419, 1941-0492
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Abstract	This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.
AbstractList	This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method. This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.
Author	Shengyuan Xu Deming Yuan Huanyu Zhao
Author_xml	– sequence: 1 surname: Deming Yuan fullname: Deming Yuan email: demingyuan@yahoo.com organization: Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China – sequence: 2 surname: Shengyuan Xu fullname: Shengyuan Xu email: syxu02@yahoo.com.cn organization: Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China – sequence: 3 surname: Huanyu Zhao fullname: Huanyu Zhao email: zhao223463@yahoo.com.cn organization: Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/21824853$$D View this record in MEDLINE/PubMed
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SubjectTerms	Algorithm design and analysis Approximation algorithms Average consensus Convergence Convex functions convex optimization distributed optimization Lagrangian functions Optimization subgradient method Upper bound
Title	Distributed Primal-Dual Subgradient Method for Multiagent Optimization via Consensus Algorithms
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