一种改进的乘子交替方向法在■正则化分裂可行问题中的应用  

An improved alternating direction method of multipliers for ℓ1-norm regularization splitting feasibility problem

作　　者：党亚峥[1] 唐崇伟 DANG Yazheng;TANG Chongwei(Business School,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学管理学院,上海200093

出　　处：《上海理工大学学报》2020年第5期460-466,503,共8页Journal of University of Shanghai For Science and Technology

摘　　要：提出了一种改进的乘子交替方向法(ADMM)算法,基于松弛技术和预测-校正框架,将松弛算子引入子问题x和对偶变量λ,使得每次迭代的步长大于1,从而提高了算法的收敛性,并在变分不等式的框架下证明了该算法的收敛性。此外,数值实验中通过图像去模糊问题验证了算法的有效性,并基于多组对照实验,综合考虑收敛效率和图像质量,选取适当的收敛准则。we proposes an improved alternating direction method of multipliers(ADMM)algorithm based on the relaxation technique and the prediction-correction framework,which introduces the new parameters in the subproblem x and the dual problemλ,so that the step size of each iteration is greater than 1,thereby improving the convergence of the algorithm.The convergence of the algorithm is proved in the framework of variational inequality.Moreover,the image deblurring problem in numerical experiments verifies that the algorithm is effective.Based on multiple sets of convergence criteria,the appropriate value is selected by comprehensively considering the rate of convergence and the quality of images.

关 键 词：ℓ1范数 改进的乘子交替方向法 松弛因子 图像模糊 

分 类 号：O221[理学—运筹学与控制论]