On the convergence rate of the bi-alternating direction method of multipliers

Publication Type:
Conference Proceeding
Citation:
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2014, pp. 3869 - 3873
Issue Date:
2014-01-01
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In this paper, we analyze the convergence rate of the bi-alternating direction method of multipliers (BiADMM). Differently from ADMM that optimizes an augmented Lagrangian function, Bi-ADMM optimizes an augmented primal-dual Lagrangian function. The new function involves both the objective functions and their conjugates, thus incorporating more information of the objective functions than the augmented Lagrangian used in ADMM. We show that BiADMM has a convergence rate of O(K-1) (K denotes the number of iterations) for general convex functions. We consider the lasso problem as an example application. Our experimetal results show that BiADMM outperforms not only ADMM, but fast-ADMM as well. © 2014 IEEE.
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