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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Bibliographic Details
Published in:IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 41; no. 6; pp. 1715 - 1724
Main Authors: Deming Yuan, Shengyuan Xu, Huanyu Zhao
Format: Journal Article
Language:English
Published: United States IEEE 01.12.2011
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1083-4419
1941-0492
DOI:10.1109/TSMCB.2011.2160394