Convergent prediction-correction-based ADMM for multi-block separable convex programming

doi:10.1016/j.cam.2017.11.033

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	Convergent prediction-correction-based ADMM for multi-block separable convex programming
	Chang, Xiaokai 1,2; Liu, Sanyang 1; Zhao, Pengjun 3; Li, Xu 2
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2018-06
卷号	335 页码:270-288
关键词	Alternating direction method of multipliers Prediction-correction Variational inequality Convergence analysis Quadratic semidefinite programming Image decomposition
ISSN号	0377-0427
DOI	10.1016/j.cam.2017.11.033
英文摘要	The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or employing proximal terms to solve inexactly the subproblems in ADMMe. In this paper, we present an efficient Prediction-Correction-based ADMM (PCB-ADMM) to solve the multi-block separable convex minimization model. The prediction step takes a special block coordinate descent (BCD) cycle to update the variable blocks, then the correction step corrects the output slightly by computing a convex combination of two points from the prediction step and previous iteration. The convergence property is obtained by using the variational inequality. The numerical experiments illustrate effectiveness of the proposed PCB-ADMM to solve the quadratic semidefinite programming and image decomposition. (C) 2017 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[61373174] ; National Natural Science Foundation of China[11501272]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000424722100017
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/32632]
专题	理学院
通讯作者	Chang, Xiaokai
作者单位	1.Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China 2.Lanzhou Univ Technol, Coll Sci, Lanzhou 730050, Gansu, Peoples R China 3.Shanglue Univ, Sch Math & Comp Applicat, Shanglue 726000, Peoples R China
推荐引用方式 GB/T 7714	Chang, Xiaokai,Liu, Sanyang,Zhao, Pengjun,et al. Convergent prediction-correction-based ADMM for multi-block separable convex programming[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2018,335:270-288.
APA	Chang, Xiaokai,Liu, Sanyang,Zhao, Pengjun,&Li, Xu.(2018).Convergent prediction-correction-based ADMM for multi-block separable convex programming.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,335,270-288.
MLA	Chang, Xiaokai,et al."Convergent prediction-correction-based ADMM for multi-block separable convex programming".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 335(2018):270-288.