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AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY
Kou, Caixia1; Chen, Zhongwen2; Dai, Yu-Hong3; Han, Haifei2
2018
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume36Issue:3Pages:331-350
AbstractAn 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.
KeywordNonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence
DOI10.4208/jcm.1705-m2016-0820
Language英语
Funding ProjectChinese NSF[11631013] ; Chinese NSF[11331012] ; Chinese NSF[71331001] ; Chinese NSF[11401038] ; Chinese NSF[11471052] ; Chinese NSF[11371273] ; National 973 Program of China[2015CB856000]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455995700002
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32257
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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