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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 Publication JOURNAL OF COMPUTATIONAL MATHEMATICS ISSN 0254-9409 Volume 36Issue:3Pages:331-350 Abstract 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. Keyword Nonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence DOI 10.4208/jcm.1705-m2016-0820 Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000455995700002 Publisher GLOBAL SCIENCE PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/32257 Collection 计算数学与科学工程计算研究所 Corresponding Author Kou, Caixia Affiliation 1.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China2.Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China Recommended CitationGB/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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