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We study distributed optimization where nodes cooperatively minimize the sumof their individual, locally known, convex costs $f_i(x)$'s, $x \in {\mathbbR}^d$ is global. Distributed augmented Lagrangian (AL) methods have goodempirical performance on several signal processing and learning applications,but there is limited understanding of their convergence rates and how itdepends on the underlying network. This paper establishes globally linear(geometric) convergence rates of a class of deterministic and randomizeddistributed AL methods, when the $f_i$'s are twice continuously differentiableand have a bounded Hessian. We give explicit dependence of the convergencerates on the underlying network parameters. Simulations illustrate ouranalytical findings.

Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms