Convergence rates for an inexact ADMM applied to separable convex optimization

William W. Hager () and Hongchao Zhang ()
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William W. Hager: University of Florida
Hongchao Zhang: Louisiana State University

Computational Optimization and Applications, 2020, vol. 77, issue 3, No 6, 729-754

Abstract: Abstract 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 $$\mathcal{{O}}(1/k)$$ O ( 1 / k ) in a convex setting and $$\mathcal{{O}}(1/k^2)$$ 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.

Keywords: Separable convex optimization; Alternating direction method of multipliers; ADMM; Accelerated gradient method; Inexact methods; Global convergence; Convergence rates; 90C06; 90C25; 65Y20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-020-00221-y

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