求解非凸两分块优化问题的Majorized Bregman交替方向乘子法  

Majorized Bregman Alternating Direction Method of Multipliers for Solving Nonconvex Two Block Optimization Problems

作　　者：陈建华 彭建文 罗洪林 CHEN Jianhua;PENG Jianwen;LUO Honglin(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2023年第5期1-10,共10页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金重大项目(No.11991024);国家自然科学基金面上项目(No.12271071);重庆英才创新创业领军人才创新创业示范团队项目(No.CQYC20210309536);重庆英才计划“包干制”项目(No.cstc2022ycjh-bgzxm0147);重庆市高校创新研究群体项目(No.CXQT20014);重庆市自然科学基金项目(No.cstc2021jcyj-msxmX0300)。

摘　　要：针对一类两分块非凸优化问题,提出Majorized带Bregman距离的交替方向乘子法。为了使问题的子问题更易求解,对目标函数中的光滑项进行极大化线性处理,并对x子问题和y子问题同时添加一个Bregman距离。在适当的假设条件下,建立了算法的全局收敛性。同时,在效益函数满足KL性质时,建立了算法的强收敛性。数值实验结果验证该算法的有效性。For a class of two block nonconvex optimization problems,a majorized alternating direction method of multipliers with Bregman distance is proposed.In order to make the subproblem of the problem easier to solve,maximizing the smooth term in the objective function with linear processing and a Bergman distance is added to the x-subproblem and the y-subproblem at the same time.Under appropriate assumptions,the global convergence of the algorithm is established.Secondly,when the benefit function satisfies the KL property,the strong convergence of the algorithm is established.Numerical experiments are carried out on the algorithm,and the results show that the algorithm is an effective method.

关 键 词：交替方向乘子法 Bregman距离 非凸优化问题 KL性质 收敛性 

分 类 号：O211.6[理学—概率论与数理统计]