Abstract
Alternating Direction Method of Multipliers (ADMM) has seen much progress in the literature in recent years. Usually, linear convergence of distributed ADMM is proved under either second-order conditions or strong convexity. When both conditions fail, an alternative is expected to play the role. In this paper, it is shown that distributed ADMM can achieve a linear convergence rate by imposing metric subregularity on a defined mapping. Furthermore, it is proved that both second-order conditions and strong convexity imply metric subregularity under reasonable conditions, e.g. the cost functions being twice continuously differentiable in a neighborhood. In addition, nonergodic convergence rates are presented as well for problems under consideration. Finally, simulation results are carried out to illustrate the efficiency of the proposed algorithm.
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