• •

1. 1. 广西民族大学理学院, 南宁 530006; 2. 广西大学数学与信息科学学院, 南宁 530004
• 出版日期:2021-11-25 发布日期:2021-12-25

JIAN Jinbao, XU Xiao, CHAO Miantao. Convergence of Proximal ADMM with an Over-Relaxation Stepsize for Nonconvex Two-Block Problem[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(11): 3139-3150.

### Convergence of Proximal ADMM with an Over-Relaxation Stepsize for Nonconvex Two-Block Problem

JIAN Jinbao1 ,XU Xiao2, CHAO Miantao2

1. 1. College of Science, Guangxi University for Nationalities, Nanning 530006; 2. College of Mathematics and Information Science, Guangxi University, Nanning 530004
• Online:2021-11-25 Published:2021-12-25

In this paper, we study the convergence of proximal alternating direction method of multipliers (PADMM) with over-relaxation stepsize parameter for nonconvex two-block optimization with linear constraints. The existing alternating direction method of multipliers all require the iteration step parameter of dual variable $\theta\in (0, \frac{1+\sqrt{5}}{2}]$. In this paper, we analyze the convergence of PADMM when $\theta\in(0,2)$. First, we prove that PADMM is globally convergent under suitable assumptions. Second, under the assumption that the merit function satisfied the Kurdyka-{\L}ojasiewicz property, we prove that the PADMM is strongly convergent. Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.
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