A proximal block minimization method of multipliers with a substitution procedure

作者：Chao, M T; Cheng, C Z; Liang, D Y^*

来源：Optimization Methods and Software, 2015, 30(4): 825-842.

DOI：10.1080/10556788.2014.992432

• block coordinate descent method
• alternating direction method of multipliers
• convex programming
• convergence rate
• contraction methods

This paper considers the problem of minimizing the sum of a smooth convex function and a separable convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal processing, wireless networking and smart grid provisioning. We propose a new algorithm called the proximal block minimization method of multipliers with a substitution to solve this family of problems. The proposed algorithm integrates the block coordinate descent and alternating direction method of multipliers with substitution. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case Omicron(1/t) convergence rate in an ergodic sense, where t denotes the number of iterations. Finally, some preliminary numerical results are reported to support the efficiency of the new algorithm.

• 出版日期2015
• 单位北京工业大学