English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

With the unprecedented growth of signal processing and machine learningapplication domains, there has been a tremendous expansion of interest indistributed optimization methods to cope with the underlying large-scaleproblems. Nonetheless, inevitable system-specific challenges such as limitedcomputational power, limited communication, latency requirements, measurementerrors, and noises in wireless channels impose restrictions on the exactness ofthe underlying algorithms. Such restrictions have appealed to the explorationof algorithms' convergence behaviors under inexact settings. Despite theextensive research conducted in the area, it seems that the analysis ofconvergences of dual decomposition methods concerning primal optimalityviolations, together with dual optimality violations is less investigated.Here, we provide a systematic exposition of the convergence of feasible pointsin dual decomposition methods under inexact settings, for an important class ofglobal consensus optimization problems. Convergences and the rate ofconvergences of the algorithms are mathematically substantiated, not only froma dual-domain standpoint but also from a primal-domain standpoint. Analyticalresults show that the algorithms converge to a neighborhood of optimality, thesize of which depends on the level of underlying distortions. Furtherelaboration of a generalized problem formulation is also furnished, togetherwith the convergence properties of the underlying algorithms. Finally,theoretical derivations are verified by numerical experiments.

On the Primal Feasibility in Dual Decomposition Methods Under Additive and Bounded Errors