Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization

doi:10.1007/s10589-016-9854-9

CSpace

	Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization
	Huang, Yakui 1,2; Liu, Hongwei 1
	2016-12-01
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
卷号	65 期号:3 页码:671-698
摘要	We present a smoothing projected Barzilai-Borwein (SPBB) algorithm for solving a class of minimization problems on a closed convex set, where the objective function is nonsmooth nonconvex, perhaps even non-Lipschitz. At each iteration, the SPBB algorithm applies the projected gradient strategy that alternately uses the two Barzilai-Borwein stepsizes to the smooth approximation of the original problem. Nonmonotone scheme is adopted to ensure global convergence. Under mild conditions, we prove convergence of the SPBB algorithm to a scaled stationary point of the original problem. When the objective function is locally Lipschitz continuous, we consider a general constrained optimization problem and show that any accumulation point generated by the SPBB algorithm is a stationary point associated with the smoothing function used in the algorithm. Numerical experiments on - problems, image restoration problems, and stochastic linear complementarity problems show that the SPBB algorithm is promising.
关键词	Smoothing projected Barzilai-Borwein algorithm Constrained non-Lipschitz optimization Nonsmooth nonconvex optimization Smoothing approximation l(2)-l(p) problem Image restoration Stochastic linear complementarity problem
DOI	10.1007/s10589-016-9854-9
语种	英语
资助项目	National Natural Science Foundation of China (NNSFC)[61072144] ; National Natural Science Foundation of China (NNSFC)[61179040] ; Fundamental Research Funds for the Central Universities[K50513100007]
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000387773500005
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/24116
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Yakui
作者单位	1.Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Huang, Yakui,Liu, Hongwei. Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2016,65(3):671-698.
APA	Huang, Yakui,&Liu, Hongwei.(2016).Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,65(3),671-698.
MLA	Huang, Yakui,et al."Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 65.3(2016):671-698.