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A NOVEL AUGMENTED LAGRANGIAN METHOD OF MULTIPLIERS FOR OPTIMIZATION WITH GENERAL INEQUALITY CONSTRAINTS

文献类型：期刊论文

作者Liu, Xin-Wei1; Dai, Yu-Hong3; Huang, Ya-Kui1; Sun, Jie1,4
刊名MATHEMATICS OF COMPUTATION
出版日期2022-12-20
页码30
ISSN号0025-5718
关键词Nonlinear programming inequality-constrained optimization augmented Lagrangian method of multipliers strong global convergence local convergence
DOI10.1090/mcom/3799
英文摘要We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented Lagrangian. A novel augmented Lagrangian method of multipliers (ALM) is then presented. Our method is originated from a generalization of the Hestenes-Powell augmented Lagrangian, and is a combination of the augmented Lagrangian and the interior-point technique. It shares a similar algorithmic framework with existing ALMs for optimization with inequality constraints, but it can use the second derivatives and does not depend on projections on the set of inequality constraints. In each iteration, our method solves a twice continuously differentiable unconstrained optimization subproblem on primal variables. The dual iterates, penalty and smoothing parameters are updated adaptively. The global and local convergence are analyzed. Without assuming any constraint qualification, it is proved that the proposed method has strong global convergence. The method may converge to either a Karush-Kuhn-Tucker (KKT) point or a singular stationary point when the converging point is a minimizer. It may also converge to an infeasible stationary point of nonlinear program when the problem is infeasible. Furthermore, our method is capable of rapidly detecting the possible infeasibility of the solved problem. Under suitable conditions, it is locally linearly convergent to the KKT point, which is consistent with ALMs for optimization with equality constraints. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results.
资助项目NSFC[12071108] ; NSFC[11671116] ; NSFC[12021001] ; NSFC[11991021] ; NSFC[11991020] ; NSFC[11971372] ; NSFC[XDA27000000] ; National Key R&D Program of China[11701137] ; National Key R&D Program of China[2021YFA 1000300] ; Strategic Priority Research Program of Chinese Academy of Sciences[2021YFA 1000301] ; Natural Science Foundation of Hebei Province[A2021202010]
WOS研究方向Mathematics
语种英语
出版者AMER MATHEMATICAL SOC
WOS记录号WOS:000903523900001
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60452]  
专题中国科学院数学与系统科学研究院
通讯作者Liu, Xin-Wei
作者单位1.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad, Sch Math Sci, Beijing 100049, Peoples R China
4.Natl Univ Singapore, Sch Business, Singapore 119245, Singapore
推荐引用方式
GB/T 7714		 Liu, Xin-Wei,Dai, Yu-Hong,Huang, Ya-Kui,et al. A NOVEL AUGMENTED LAGRANGIAN METHOD OF MULTIPLIERS FOR OPTIMIZATION WITH GENERAL INEQUALITY CONSTRAINTS[J]. MATHEMATICS OF COMPUTATION,2022:30.
APA Liu, Xin-Wei,Dai, Yu-Hong,Huang, Ya-Kui,&Sun, Jie.(2022).A NOVEL AUGMENTED LAGRANGIAN METHOD OF MULTIPLIERS FOR OPTIMIZATION WITH GENERAL INEQUALITY CONSTRAINTS.MATHEMATICS OF COMPUTATION,30.
MLA Liu, Xin-Wei,et al."A NOVEL AUGMENTED LAGRANGIAN METHOD OF MULTIPLIERS FOR OPTIMIZATION WITH GENERAL INEQUALITY CONSTRAINTS".MATHEMATICS OF COMPUTATION (2022):30.

入库方式： OAI收割

来源：数学与系统科学研究院

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