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Convergence rates for an inexact ADMM applied to separable convex optimization
Convergence rates are established for an inexact accelerated alternating
direction method of multipliers (I-ADMM) for general separable convex
optimization with a linear constraint. Both ergodic and non-ergodic iterates
are analyzed. Relative to the iteration number k, the convergence rate is
O(1/k) in a convex setting and O(1/k^2) in a strongly convex setting. When an
error bound condition holds, the algorithm is 2-step linearly convergent. The
I-ADMM is designed so that the accuracy of the inexact iteration preserves the
global convergence rates of the exact iteration, leading to better numerical
performance in the test problems.Comment: arXiv admin note: text overlap with arXiv:1604.0249