Primal–dual algorithm for distributed constrained optimization

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraints assigned to the agents. Based on the augmented...

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Bibliographic Details
Published in:	Systems & control letters Vol. 96; pp. 110 - 117
Main Authors:	Lei, Jinlong, Chen, Han-Fu, Fang, Hai-Tao
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.10.2016
Subjects:	Augmented Lagrange method Distributed constrained optimization Multi-agent network Primal–dual algorithm Augmented Lagrange method Distributed constrained optimization Multi-agent network Primal–dual algorithm
ISSN:	0167-6911, 1872-7956
Online Access:	Get full text
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Summary:	The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraints assigned to the agents. Based on the augmented Lagrange method, a distributed primal–dual algorithm with a projection operation included is proposed to solve the problem. It is shown that with appropriately chosen constant step size, the local estimates derived at all agents asymptotically reach a consensus at an optimal solution. In addition, the value of the cost function at the time-averaged estimate converges with rate O(1k) to the optimal value for the unconstrained problem. By these properties, the proposed primal–dual algorithm is distinguished from the existing algorithms for distributed constrained optimization. The theoretical analysis is justified by numerical simulations.
ISSN:	0167-6911 1872-7956
DOI:	10.1016/j.sysconle.2016.07.009