A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming

doi:10.1080/02331934.2018.1490956

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	A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming
	Chang, Xiaokai 1,2; Liu, Sanyang 2; Zhao, Pengjun 3
刊名	OPTIMIZATION
	2018
卷号	67 期号:10 页码:1729-1743
关键词	Alternating direction method of multipliers semidefinite programming H-weighted nearest correlation matrix problem convergence analysis
ISSN号	0233-1934
DOI	10.1080/02331934.2018.1490956
英文摘要	In this note, we consider three types of problems, H-weighted nearest correlation matrix problem and two types of important doubly non-negative semidefinite programming, derived from the binary integer quadratic programming and maximum cut problem. The dual of these three types of problems is a 3-block separable convex optimization problem with a coupling linear equation constraint. It is known that, the directly extended 3-block alternating direction method of multipliers (ADMM3d) is more efficient than many of its variants for solving these convex optimization, but its convergence is not guaranteed. By choosing initial points properly, we obtain the convergence of ADMM3d for solving the dual of these three types of problems. Furthermore, we simplify the iterative scheme of ADMM3d and show the equivalence of ADMM3d to the 2-block semi-proximal ADMM for solving the dual's reformulation, under these initial conditions.
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000452281300010
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/32915]
专题	理学院
通讯作者	Chang, Xiaokai
作者单位	1.Lanzhou Univ Technol, Coll Sci, Lanzhou 730050, Gansu, Peoples R China 2.Xidian Univ, Sch Math & Stat, Xian, Shaanxi, Peoples R China 3.Shanglue Univ, Sch Math & Comp Applicat, Shanglue, Peoples R China
推荐引用方式 GB/T 7714	Chang, Xiaokai,Liu, Sanyang,Zhao, Pengjun. A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming[J]. OPTIMIZATION,2018,67(10):1729-1743.
APA	Chang, Xiaokai,Liu, Sanyang,&Zhao, Pengjun.(2018).A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming.OPTIMIZATION,67(10),1729-1743.
MLA	Chang, Xiaokai,et al."A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming".OPTIMIZATION 67.10(2018):1729-1743.