| 引用本文： |
-
邓钊,晁绵涛,简金宝.非凸两分块问题乘子交替方向法的收敛性分析[J].广西科学,2016,23(5):422-427. [点击复制]
- DENG Zhao,CHAO Miantao,JIAN Jinbao.Convergence Analysis of Alternating Direction Method of Multipliers for Two Block Nonconvex Problems[J].Guangxi Sciences,2016,23(5):422-427. [点击复制]
|
|
| 摘要: |
| 乘子交替方向法(ADMM)求解大规模问题十分有效.ADMM在凸情形下的收敛性已被清晰认识,但非凸问题ADMM的收敛性结果还很少.本文针对非凸两分块优化问题,在增广拉格朗日函数满足Kurdyka-Lojasiewicz不等式性质且罚参数大于某个常数的条件下,证明了ADMM的收敛性. |
| 关键词: 乘子交替方向法 Kurdyka-Lojasiewicz不等式 非凸优化 收敛性 |
| DOI：10.13656/j.cnki.gxkx.20161121.005 |
| 投稿时间：2016-07-01修订日期：2016-10-27 |
| 基金项目:国家自然科学基金项目(11601095),广西自然科学基金项目(2014GXNSFFA118001,2016GXNSFDA380019)和广西高校科研项目(ZD201407)资助。 |
|
| Convergence Analysis of Alternating Direction Method of Multipliers for Two Block Nonconvex Problems |
|
DENG Zhao1, CHAO Miantao1, JIAN Jinbao2
|
| (1.College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China;2.School of Mathematics and Statistics, Yulin Normal University, Yulin, Guangxi, 537000, China) |
| Abstract: |
| The Alternating Direction Method of Multipliers(ADMM) is an effective method for large scale optimization problems.While the convergence of ADMM has been clearly recognized in the case of convex,the convergence result of ADMM in the case of nonconvex is still an open problem.In this paper,under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality and the penalty parameter is greater than a constant,we analyze the convergence of ADMM for a class of nonconvex optimization problems whose objective function is the sum of two block nonconvex functions. |
| Key words: Alternating Direction Method of Multipliers Kurdyka-Lojasiewicz inequality nonconvex optimization convergence |
