Gradient methods exploiting spectral properties

doi:10.1080/10556788.2020.1727476

	Gradient methods exploiting spectral properties
	Huang, Yakui 2; Dai, Yu-Hong 3; Liu, Xin-Wei 2; Zhang, Hongchao 1
刊名	OPTIMIZATION METHODS & SOFTWARE
	2020-02-15
页码	25
关键词	Gradient methods spectral property Barizilai-Borwein method linear convergence quadratic optimization bound constrained optimization
ISSN号	1055-6788
DOI	10.1080/10556788.2020.1727476
英文摘要	We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's asymptotic optimal gradient method (Computational Optimization and Applications, 2006, 33(1): 73-88) is applied for minimizing quadratic objective functions. Based on this spectral property, we develop a monotone gradient method that takes a certain number of steps using the asymptotically optimal stepsize by Dai and Yang, and then follows by some short steps associated with this new stepsize. By employing one step retard of the asymptotic optimal stepsize, a nonmonotone variant of this method is also proposed. Under mild conditions, R-linear convergence of the proposed methods is established for minimizing quadratic functions. In addition, by combining gradient projection techniques and adaptive nonmonotone line search, we further extend those methods for general bound constrained optimization. Two variants of gradient projection methods combining with the Barzilai-Borwein stepsizes are also proposed. Our numerical experiments on both quadratic and bound constrained optimization indicate that the new proposed strategies and methods are very effective.
资助项目	National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11671116] ; National 973 Program of China[2015CB856002] ; China Scholarship Council[201806705007] ; USA National Science Foundation[1522654] ; USA National Science Foundation[1819161]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000514512500001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50834]
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, Yu-Hong
作者单位	1.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA 2.Hebei Univ Technol, Inst Math, Tianjin, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,et al. Gradient methods exploiting spectral properties[J]. OPTIMIZATION METHODS & SOFTWARE,2020:25.
APA	Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,&Zhang, Hongchao.(2020).Gradient methods exploiting spectral properties.OPTIMIZATION METHODS & SOFTWARE,25.
MLA	Huang, Yakui,et al."Gradient methods exploiting spectral properties".OPTIMIZATION METHODS & SOFTWARE (2020):25.