Convergence Analysis of Dual Decomposition Algorithm in Distributed Optimization: Asynchrony and Inexactness
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Date
2023-08Type
- Journal Article
Abstract
Dual decomposition is widely utilized in the distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet drop. In addition, computational errors also exist when the individual agents solve their own subproblems. In this paper, we analyze the convergence of the dual decomposition algorithm in the distributed optimization when both the communication asynchrony and the subproblem solution inexactness exist. We find that the interaction between asynchrony and inexactness slows down the convergence rate from O(1/k) to O(1/√k). Specifically, with a constant step size, the value of the objective function converges to a neighborhood of the optimal value, and the solution converges to a neighborhood of the optimal solution. Moreover, the violation of the constraints diminishes in O(1/√k). Our result generalizes and unifies the existing ones that only consider either asynchrony or inexactness. Finally, numerical simulations validate the theoretical results. Show more
Publication status
publishedExternal links
Journal / series
IEEE Transactions on Automatic ControlVolume
Pages / Article No.
Publisher
IEEESubject
Asynchronous algorithm; distributed optimization; dual decomposition; inexact algorithm; multi-agent systemOrganisational unit
09481 - Hug, Gabriela / Hug, Gabriela
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