University of Oulu

H. Abeynanda, C. Weeraddana, G. H. J. Lanel and C. Fischione, "On the Primal Feasibility in Dual Decomposition Methods Under Additive and Bounded Errors," in IEEE Transactions on Signal Processing, vol. 71, pp. 655-669, 2023, doi: 10.1109/TSP.2023.3249043

On the primal feasibility in dual decomposition methods under additive and bounded errors

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Author: Abeynanda, Hansi1; Weeraddana, Chathuranga2; Lanel, G. H. J.3;
Organizations: 1School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden
2Centre for Wireless Communication, University of Oulu, Oulu, Finland
3Department of Mathematics, University of Sri Jayewardenepura, Nugegoda, Sri Lanka
4School of Electrical Engineering and Computer Science and Digital Futures, KTH Royal Institute of Technology, Stockholm, Sweden
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.9 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2023
Publish Date: 2023-04-27


With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems. Nonetheless, inevitable system-specific challenges such as limited computational power, limited communication, latency requirements, measurement errors, and noises in wireless channels impose restrictions on the exactness of the underlying algorithms. Such restrictions have appealed to the exploration of algorithms' convergence behaviors under inexact settings. Despite the extensive research conducted in the area, it seems that the analysis of convergences of dual decomposition methods concerning primal optimality violations, together with dual optimality violations is less investigated. Here, we provide a systematic exposition of the convergence of feasible points in dual decomposition methods under inexact settings, for an important class of global consensus optimization problems. Convergences and the rate of convergences of the algorithms are mathematically substantiated, not only from a dual-domain standpoint but also from a primal-domain standpoint. Analytical results show that the algorithms converge to a neighborhood of optimality, the size of which depends on the level of underlying distortions.

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Series: IEEE transactions on signal processing
ISSN: 1053-587X
ISSN-E: 1941-0476
ISSN-L: 1053-587X
Volume: 71
Pages: 655 - 669
DOI: 10.1109/tsp.2023.3249043
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Funding: The work of Hansi Abeynanda and Carlo Fischione was supported in part by the SSF Project SAICOM and in part by VR MALEN.
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