[1]申远,夏书育.自适应步长带回代的邻近分块乘子极小化算法[J].西华师范大学学报(自然科学版),2019,40(02):141-148.[doi:10.16246/j.issn.1673-5072.2019.02.007]
 SHEN Yuan,XIA Shuyu.Proximal Block Multiplier Minimization Algorithm withAdaptive Step Size and Substitution Procedure[J].Journal of China West Normal University(Natural Sciences),2019,40(02):141-148.[doi:10.16246/j.issn.1673-5072.2019.02.007]
点击复制

自适应步长带回代的邻近分块乘子极小化算法

()
分享到:

《西华师范大学学报(自然科学版)》[ISSN:1673-5072/CN:51-1699/N]

卷:
40
期数:
2019年02期
页码:
141-148
栏目:
出版日期:
2019-06-20

文章信息/Info

Title:

Proximal Block Multiplier Minimization Algorithm withAdaptive Step Size and Substitution Procedure

作者:

申远 夏书育

(南京财经大学 应用数学学院,南京210023)

Author(s):

SHEN YuanXIA Shuyu

(School of Applied Mathematics,Nanjing University of Finance & Economics,Nanjing Jiangsu 210023,China)

关键词:

目标函数可分离块坐标下降法交替方向乘子法自适应步长

Keywords:

separable object functionblock coordinate descent methodalternating direction method of multipliersadaptive step size

分类号:
O221.2;O224
DOI:
10.16246/j.issn.1673-5072.2019.02.007
文献标志码:
A
摘要:

本文考虑求解带线性约束的多块凸优化问题,其中的目标函数有一项不可分离。对于目标函数中存在不可分离项,晁绵涛等人将块坐标下降法与交替方向乘子法相结合提出了PBMM-MS算法,并通过数值实验验证了其有效性。本文对PBMM-MS算法进行改进,提出了自适应步长带回代的邻近分块乘子极小化算法,该算法结合了步长的自适应调整技术,使步长在迭代过程中自动调整,提高了算法的计算效率。对于提出的算法,我们证明了其收敛性。

Abstract:

This paper talks about solving multi-block convex optimization problems with linear constraints,among which is the inseparable term of object function.To solve the problem,Chao miautao et al.hewe proposed a PBMM-MS algorithm by integrating block coordinate descent method with alternating direction method of multipliers,and verified its validity via numerical experiments.Based on PBMM-MS algorithm,a new algorithm with adaptive step size and substitution procedure is proposed.The algorithm adopts the adaptive step size technique that enables automatical adjustment of the step size during the iterative process.Hence,the computational efficiency of the algorithm is improved.In addition,global convergence of the proposed algorithm is also derived.

备注/Memo

备注/Memo:

收稿日期:2018-10-12
基金项目:国家社科基金一般项目(17BTQ063);江苏省社科基金重点项目(18GLA002);江苏省青蓝工程。
作者简介:申  远(1982—),男,江苏南京人,博士,副教授,硕士生导师,主要从事最优化算法发研究。
通信作者:申远,E-mail:ocsiban@126.com

更新日期/Last Update: 2019-06-25