AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY

doi:10.4208/jcm.1705-m2016-0820

	AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY
	Kou, Caixia 1; Chen, Zhongwen 2; Dai, Yu-Hong3 ; Han, Haifei 2
	2018
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	36 期号:3 页码:331-350
摘要	An augmented Lagrangian trust region method with a bi-object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
关键词	Nonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence
DOI	10.4208/jcm.1705-m2016-0820
语种	英语
资助项目	Chinese NSF[11631013] ; Chinese NSF[11331012] ; Chinese NSF[71331001] ; Chinese NSF[11401038] ; Chinese NSF[11471052] ; Chinese NSF[11371273] ; National 973 Program of China[2015CB856000]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455995700002
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32257
专题	计算数学与科学工程计算研究所
通讯作者	Kou, Caixia
作者单位	1.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China 2.Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Kou, Caixia,Chen, Zhongwen,Dai, Yu-Hong,et al. AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2018,36(3):331-350.
APA	Kou, Caixia,Chen, Zhongwen,Dai, Yu-Hong,&Han, Haifei.(2018).AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY.JOURNAL OF COMPUTATIONAL MATHEMATICS,36(3),331-350.
MLA	Kou, Caixia,et al."AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY".JOURNAL OF COMPUTATIONAL MATHEMATICS 36.3(2018):331-350.