Convergence Analysis of a Distributed Optimization Algorithm with a General Unbalanced Directed Communication Network

In this paper, we discuss a class of distributed constrained optimization problems in power systems where the target is to optimize the sum of all agents’ local convex objective functions over a general unbalanced directed communication network. Each local convex objective function is known exclusiv...

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Veröffentlicht in:IEEE transactions on network science and engineering Jg. 6; H. 3; S. 237 - 248
Hauptverfasser: Li, Huaqing, Lu, Qingguo, Huang, Tingwen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 01.07.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Communication
Communication networks
Communications networks
Constraints
Convergence
Convexity
Coupling
Couplings
Distributed constrained optimization
Economic models
Linear programming
Load management
Mathematical analysis
Optimization
Power systems
primal-dual (sub)gradient algorithm
Smoothness
unbalanced directed network
uncoordinated step-sizes
Upper bounds
ISSN:2327-4697, 2334-329X
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Zusammenfassung:In this paper, we discuss a class of distributed constrained optimization problems in power systems where the target is to optimize the sum of all agents’ local convex objective functions over a general unbalanced directed communication network. Each local convex objective function is known exclusively to a single agent, and the agents’ variables are constrained to global coupling linear constraint and individual box constraints. To collaboratively solve the optimization problems, existing distributed methods mostly require the communication network to be balanced or have the knowledge of in-neighbors’ out-degree for all agents, which are quite restrictive and hardly inevitable in practical applications. In contrast, we investigate a novel distributed primal-dual augmented (sub)gradient algorithm which utilizes a row-stochastic matrix (does not need each agent to know its in-neighbors out-degree) and employs uncoordinated step-sizes, and yet exactly converges to the optimal solution over a general unbalanced directed communication network. Under the assumptions of the strong convexity and smoothness on the aggregate objective functions, it is proved that the algorithm geometrically converges to the optimal solution if the uncoordinated step-sizes do not exceed the upper bound. An explicit analysis for the convergence rate of the proposed algorithm is also characterized. To manifest effectiveness and applicability of the proposed algorithm, three case studies are presented to solve two practical problems in power systems.
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ISSN:2327-4697
2334-329X
DOI:10.1109/TNSE.2018.2848288