IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS

doi:10.1142/S0217595910002594

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	IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS
	Fu, Yun-Shan; Dai, Yu-Hong
刊名	ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
	2010-02-01
卷号	27 期号:1 页码:71-84
关键词	Monotone projected gradient algorithm Support Vector Machine (SVM) adaptive steepest descent step-size Dai-Yuan step-size projection subproblem
ISSN号	0217-5959
DOI	10.1142/S0217595910002594
英文摘要	In this paper, we consider the projected gradient algorithms for solving the quadratic program with bound constraints and a single linear equality constraint (SLBQP). We establish the relationship between the Lagrangian multiplier in the projection subproblem and the Lagrangian multiplier in the original optimization problem. Then we give an improved initial estimate of the Lagrangian multiplier in the subproblem based on this relationship. It appears that this initial estimate is very close to the optimal Lagrangian multiplier after several iterations of the outer loop. This will reduce at most 40% of the computing time in the projection subproblem. This initial guess can also be used in all kinds of projected gradient methods for solving the SLBQP problem. The numerical results show that it brings much more improvement in monotone algorithms than in nonmonotone algorithms. We also apply the adaptive steepest descent step-size and the Dai-Yuan step-size which are two monotone step-sizes to the projected gradient method of this SLBQP problem. Our numerical experiments showed that their performance can be better than some other monotone projected gradient methods.
资助项目	Chinese NSF[10571171] ; Chinese NSF[10831006] ; CAS[kjcx-yw-s7-03]
WOS研究方向	Operations Research & Management Science
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000276687000006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/11209]
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Yu-Hong
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Fu, Yun-Shan,Dai, Yu-Hong. IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS[J]. ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH,2010,27(1):71-84.
APA	Fu, Yun-Shan,&Dai, Yu-Hong.(2010).IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS.ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH,27(1),71-84.
MLA	Fu, Yun-Shan,et al."IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS".ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 27.1(2010):71-84.