Title :
On the convergence rate of the bi-alternating direction method of multipliers
Author :
Guoqiang Zhang ; Heusdens, Richard ; Kleijn, W. Bastiaan
Author_Institution :
Dept. of Intell. Syst., Delft Univ. of Technol., Delft, Netherlands
Abstract :
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 experimental results show that BiADMM outperforms not only ADMM, but fast-ADMM as well.
Keywords :
convergence of numerical methods; convex programming; function approximation; iterative methods; BiADMM; augmented primal-dual Lagrangian function; bialternating direction method of multipliers; conjugates; convergence rate; general convex functions; lasso problem; objective functions; Convergence; Convex functions; Lagrangian functions; Linear programming; Optimization; Signal processing; Signal processing algorithms; Distributed optimization; alternating direction method of multipliers; bi-alternating direction of multipliers;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on
Conference_Location :
Florence
DOI :
10.1109/ICASSP.2014.6854326