Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints

doi:10.1007/s10543-015-0563-z

	Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints
	Bai, Zhong-Zhi1 ; Tao, Min 2
	2016-06-01
发表期刊	BIT NUMERICAL MATHEMATICS
ISSN	0006-3835
卷号	56 期号:2 页码:399-422
摘要	We discuss unique solvability of the equality-constraint quadratic programming problem, establish a class of preconditioned alternating variable minimization with multiplier (PAVMM) methods for iteratively computing its solution, and demonstrate asymptotic convergence property of these PAVMM methods. We also discuss an algebraic derivation of the PAVMM method by making use of matrix splitting, which reveals that the PAVMM method is actually a modified block Gauss-Seidel iteration method for solving the augmented Lagrangian linear system resulting from the weighted Lagrangian function with respect to the equality-constraint quadratic programming problem.
关键词	Equality-constraint quadratic programming problem Solvability Iteration method Preconditioning Asymptotic convergence
DOI	10.1007/s10543-015-0563-z
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000376580200002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22799
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China 2.Nanjing Univ, Dept Math, Nanjing 210008, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Tao, Min. Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints[J]. BIT NUMERICAL MATHEMATICS,2016,56(2):399-422.
APA	Bai, Zhong-Zhi,&Tao, Min.(2016).Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints.BIT NUMERICAL MATHEMATICS,56(2),399-422.
MLA	Bai, Zhong-Zhi,et al."Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints".BIT NUMERICAL MATHEMATICS 56.2(2016):399-422.