Convergence rates for an inexact ADMM applied to separable convex optimization

Authors

William W. Hager, University of Florida
Hongchao Zhang, Louisiana State University

Document Type

Article

Publication Date

12-1-2020

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 O(1 / k) in a convex setting and O(1 / k²) 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.

Publication Source (Journal or Book title)

Computational Optimization and Applications

First Page

729

Last Page

754

Recommended Citation

Hager, W., & Zhang, H. (2020). Convergence rates for an inexact ADMM applied to separable convex optimization. Computational Optimization and Applications, 77 (3), 729-754. https://doi.org/10.1007/s10589-020-00221-y