A parallel line searchsubspace correction method for composite convex optimization

CSpace

	A parallel line searchsubspace correction method for composite convex optimization
其他题名	aparallellinesearchsubspacecorrectionmethodforcompositeconvexoptimization
	Dong Qian 1; Liu Xin 1; Wen Zaiwen 2; Yuan Yaxiang 1
	2015
发表期刊	journaloftheoperationsresearchsocietyofchina
ISSN	2194-668X
卷号	3 期号:2 页码:163
摘要	In this paper, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new point along this direction using a step size satisfying the Armijo line search condition. They are called PSCLN and PSCLO, respectively, depending on whether there are overlapping regions between two imme-diately adjacent blocks of variables. Their convergence is established under mild assumptions. We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the ?_1-regularized minimization problems. Our numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test problems. It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.
其他摘要	In this paper, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new point along this direction using a step size satisfying the Armijo line search condition. They are called PSCLN and PSCLO, respectively, depending on whether there are overlapping regions between two imme-diately adjacent blocks of variables. Their convergence is established under mild assumptions. We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the ?_1-regularized minimization problems. Our numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test problems. It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.
关键词	Line search Block coordinate descent method Domain decomposition Jacobian-type iteration Distributed optimization
收录类别	CSCD
语种	英语
CSCD记录号	CSCD:5539087
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52753
专题	中国科学院数学与系统科学研究院
作者单位	1.中国科学院数学与系统科学研究院 2.北京大学
推荐引用方式 GB/T 7714	Dong Qian,Liu Xin,Wen Zaiwen,et al. A parallel line searchsubspace correction method for composite convex optimization[J]. journaloftheoperationsresearchsocietyofchina,2015,3(2):163.
APA	Dong Qian,Liu Xin,Wen Zaiwen,&Yuan Yaxiang.(2015).A parallel line searchsubspace correction method for composite convex optimization.journaloftheoperationsresearchsocietyofchina,3(2),163.
MLA	Dong Qian,et al."A parallel line searchsubspace correction method for composite convex optimization".journaloftheoperationsresearchsocietyofchina 3.2(2015):163.