62 research outputs found
A General Analysis of the Convergence of ADMM
We provide a new proof of the linear convergence of the alternating direction
method of multipliers (ADMM) when one of the objective terms is strongly
convex. Our proof is based on a framework for analyzing optimization algorithms
introduced in Lessard et al. (2014), reducing algorithm convergence to
verifying the stability of a dynamical system. This approach generalizes a
number of existing results and obviates any assumptions about specific choices
of algorithm parameters. On a numerical example, we demonstrate that minimizing
the derived bound on the convergence rate provides a practical approach to
selecting algorithm parameters for particular ADMM instances. We complement our
upper bound by constructing a nearly-matching lower bound on the worst-case
rate of convergence.Comment: 10 pages, 6 figure
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