具有线性化技术的三块非凸不可分优化问题Bregman ADMM收敛性分析

具有线性化技术的三块非凸不可分优化问题Bregman ADMM收敛性分析

Convergence Analysis of Bregman ADMM for Three-Block Nonconvex Indivisible Optimization Problems with Linearization Technique

摘要/Abstract

参考文献 27

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数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 291-304.

刘富勤,彭建文^*(),罗洪林

重庆师范大学数学科学学院重庆401331

收稿日期:2022-03-31 修回日期:2022-08-05 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*彭建文, E-mail: jwpeng168@hotmail.com
基金资助:
国家自然科学基金重大项目(11991024);国家自然科学基金面上项目(12271071);重庆英才 $\cdot$ 创新创业领军人才 $\cdot$ 创新创业示范团队项目(CQYC20210309536);重庆英才计划包干制项目(cstc2022ycjh-bgzxm0147);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金项目(cstc2021jcyj-msxmX0300)

Liu Fuqin,Peng Jianwen^*(),Luo Honglin

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2022-03-31 Revised:2022-08-05 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11991024);The NSFC(12271071);Team Project of Innovation Leading Talent in Chongqing(CQYC20210309536);Contract System Project of Chongqing Talent Plan(cstc2022ycjh-bgzxm0147);Chongqing University Innovation Research Group Project(CXQT20014);Chongqing Natural Science Foundation Project(cstc2021jcyj-msxmX0300)

摘要：

交替方向乘子法是求解两块可分离凸优化问题的有效方法, 但是对于三块不可分的非凸优化问题的交替方向乘子法的收敛性可能无法保证. 该文主要研究的是用线性化广义Bregman交替方向乘子法(L-G-BADMM)求解目标函数是三块不可分的非凸极小化问题的收敛性分析. 在适当假设条件下, 对算法中子问题进行求解并构建满足Kurdyka-Lojasiewicz性质的效益函数, 经过理论证明可以得到该算法的收敛性.

关键词: Bregman散度, 交替方向乘子法, Kurdyka-?ojasiewicz性质, 线性化

Abstract:

Alternating direction multiplier method is an effective method to solve two separable convex optimization problems, but the convergence of alternating direction multiplier method may not be guaranteed for three nonseparable nonconvex optimization problems. This paper mainly studies the convergence analysis of the linearized generalized Bregman alternating direction multiplier method (L-G-BADMM) for solving the nonconvex minimization problem whose objective function is three indivisible blocks. Under appropriate assumptions, we solve the subproblem of the algorithm and construct a benefit function satisfying Kurdyka-Lojasiewicz property. The convergence of the algorithm can be obtained through theoretical proof.

Key words: Bregman divergence, ADMM, Kurdyka-Lojasiewicz property, Linearization

中图分类号:

O221.2

刘富勤, 彭建文, 罗洪林. 具有线性化技术的三块非凸不可分优化问题Bregman ADMM收敛性分析[J]. 数学物理学报, 2023, 43(1): 291-304.

Liu Fuqin, Peng Jianwen, Luo Honglin. Convergence Analysis of Bregman ADMM for Three-Block Nonconvex Indivisible Optimization Problems with Linearization Technique[J]. Acta mathematica scientia,Series A, 2023, 43(1): 291-304.

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