分裂可行性问题的外推加速线性交替方向乘子法及其全局收敛性  

Extrapolation Accelerated Linear Alternating Direction Multiplier Method for Split Feasibility Problems and Its Global Convergence

作　　者：刘洋[1,2] 薛中会[3] 王永全 曹永胜[1] LIU Yang;XUE Zhonghui;WANG Yongquan;CAO Yongsheng(Department of Intelligent Science and Information Law,East China University of Political Science and Law,Shanghai 201620,China;China Institute for Smart Court,Shanghai Jiao Tong University,Shanghai 200030,China;Department of Information and Intelligent Engineering,Shanghai Publishing and Printing College,Shanghai 200093,China)

机构地区：[1]华东政法大学智能科学与信息法学系,上海201620 [2]上海交通大学智慧法院研究院,上海200030 [3]上海出版印刷高等专科学校信息与智能工程系,上海200093

出　　处：《计算机科学》2023年第6期261-265,共5页Computer Science

基　　金：国家社科基金重大项目(20&ZD199,21&ZD200);教育部人文社科青年基金项目(20YJC820030);国家新闻出版署“智能与绿色柔板印刷”重点实验室招标课题(KLIGFP-02)。

摘　　要：针对在图像重建以及语言处理系统等领域有着广泛应用的分裂可行性问题(SFP)的最优化求解,提出了外推加速线性交替方向乘子法。首先将SFP描述为一个具有线性约束的可分离凸极小化问题;然后引进外推线性交替方向乘子法,利用问题的可分离结构,产生了具有闭式解的子问题,并在适当条件下证明了该算法的全局收敛性;最后,通过数值实验验证了该算法的可行性和有效性。This paper deals with a linear alternating direction multiplier method(ADMM)for Split feasibility problems(SFP).More specifically,the SFP has been formulated as a separable convex minimization problem with linear constraints,and then extrapolation accelerated linear ADMM has been proposed,which takes advantage of the separable structure,and then rising to sub-problems with closed-form solutions have been given.Furthermore,the global convergence of the proposed method is proved under some suitable conditions.Moreover,the algorithm has been tested by applying to two SFP examples in our theoretical results.

关 键 词：分裂可行性问题 线性交替方向乘子法 凸极小化问题 外推加速 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]