• 论文 •

### 一类自适应广义交替方向乘子法

1. 南京师范大学数学科学学院, 南京 210023
• 收稿日期:2018-01-13 出版日期:2018-12-15 发布日期:2018-11-20
• 基金资助:

国家自然科学基金青年项目（11401315），国家自然科学基金项目（11571178）.

Jiang Fan, Liu Yamei, Cai Xingju. A SELF-ADAPTIVE GENERALIZED ALTERNATING DIRECTION METHOD OF MULTIPLIERS[J]. Mathematica Numerica Sinica, 2018, 40(4): 367-386.

### A SELF-ADAPTIVE GENERALIZED ALTERNATING DIRECTION METHOD OF MULTIPLIERS

Jiang Fan, Liu Yamei, Cai Xingju

1. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
• Received:2018-01-13 Online:2018-12-15 Published:2018-11-20

Generalized alternating direction method of multipliers (G-ADMM) is effective in solving the convex optimization problem. When the subproblem is difficult to solve in practical problem, we can add the proximal term in the subproblem. The positive definiteness of the proximal matrix guarantees the convergence while resulting in the tiny step size. A new study indicates that the proximal matrix can be indefinite. In this paper, based on the frame of G-ADMM with indefinite proximal term, we propose a self-adaptive G-ADMM while the proximal matrix is dynamically selected to increase the step size. Under mild assumptions, we prove the global convergence of the proposed method. The preliminary numerical results indicate that the new algorithm is efficient.

MR(2010)主题分类:

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