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
	2018-06-01
卷号	335 页码:270-288
关键词	Convex optimization Iterative methods Organic pollutants Polychlorinated biphenyls Variational techniques Alternating direction method of multipliers Convergence analysis Image decomposition Quadratic semidefinite programming Variational inequalities
ISSN号	03770427
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. © 2017 Elsevier B.V.
WOS研究方向	Mathematics
语种	英语
出版者	Elsevier B.V., Netherlands
WOS记录号	WOS:000424722100017
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/114587]
专题	理学院
作者单位	1.School of Mathematics and Statistics, Xidian University, Xi'an; 710071, China; 2.College of Science, Lanzhou University of Technology, Gansu; Lanzhou; 730050, China; 3.School of Mathematics and Computer Application, Shanglue University, Shanglue; 726000, 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.