A Linearized Alternating Direction Method of Multipliers with Substitution Procedure

作者：Chao Miantao^*; Cheng Caozong; Zhang Haibin

来源：Asia Pacific Journal of Operational Research, 2015, 32(3): 1550011.

DOI：10.1142/S0217595915500116

• Alternating direction method of multipliers
• convex programming
• convergence rate
• contraction methods

We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m >= 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m >= 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

• 出版日期2015-6
• 单位北京工业大学