Abstract:
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 primaldomain standpoint. Analytical results show that the algorithms
converge to a neighborhood of optimality, the size of which
depends on the level of underlying distortions.
