Distributed Optimization Under Unbalanced Digraphs With Node Errors: Robustness of Surplus-Based Dual Averaging Algorithm

In this article, the robustness of distributed constrained optimization algorithms for weight-unbalanced directed multiagent networks is studied. Specifically, it is assumed that each agent is subject to additive random node errors , which are caused by the imperfect communication in networks. Under...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 8; no. 1; pp. 331 - 341
Main Authors: Shi, Chong-Xiao, Yang, Guang-Hong
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
Algorithms
Attenuation
Control systems
Convergence
Distributed constrained optimization
Gradient methods
Graph theory
Multiagent systems
node errors
Nodes
Optimization
Protocols
Random processes
Robustness
unbalanced digraphs
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:In this article, the robustness of distributed constrained optimization algorithms for weight-unbalanced directed multiagent networks is studied. Specifically, it is assumed that each agent is subject to additive random node errors , which are caused by the imperfect communication in networks. Under this framework, it is shown that a typical algorithm, called surplus-based dual averaging (SDA), can successfully achieve the convergence to the optimal value of the considered optimization problem, which exhibits the robustness to the node errors. Technically, in the proof of this result, an important augmentation of the node errors in the fusion and surplus variables is first introduced, and then by means of the random process theory and the attenuation effect of diminishing step size on node errors, the robustness of SDA is proved. In addition, inspired by the SDA, a robust algorithm is developed to solve the distributed online optimization problem with node errors. Finally, simulations are given to verify the theoretical results.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2020.3011837