Bi-alternating direction method of multipliers

The alternating-direction method of multipliers (ADMM) has been widely applied in the field of distributed optimization and statistic learning. ADMM iteratively approaches the saddle point of an augmented Lagrangian function by performing three updates per-iteration. In this paper, we propose a bi-alternating direction method of multipliers (BiADMM) that iteratively minimizes an augmented bi-conjugate function. As a result, the convergence of BiADMM is naturally established. Unlike ADMM that always involves three updates per iteration, BiADMM opens up an avenue to perform either two or three updates per iteration, depending on the functional construction. As an application, we consider applying BiADMM for the lasso problem. Experimental results demonstrate the effectiveness of our new method.