A Hybrid type ADMM for Multi-Block Separable Convex Programming

Abstract

The alternating direction method of multiplier (ADMM) is a popular method for solving composite convex minimization problems with separable linear constraints. Unfortunately, the direct extension of the ADMM for multi-block problems is not necessarily convergent. To address this issue, several variants of the ADMM were proposed, among which the parallel splitting algorithm has attracted much attention due to its efficiency and simplicity. However, a major drawback of the parallel splitting algorithm is that the weighting factor placed on the proximal term has to be greater than a certain value in order to ensure the convergence. A large weighting factor has the effect of forcing the current solution to stay close to its previous solution, thus leading to a slow convergence speed. In this paper, we propose a new hybrid type ADMM for multi-block separable convex programming. The proposed method places a much smaller weighting factor on the proximal term. Thus the proposed algorithm has the potential to achieve faster convergence rates. Numerical results are provided to illustrate the efficiency of the proposed algorithm.