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Study on convex optimization with least constraint violation under a general measure
Dai, Yu-Hong1,2; Zhang, Liwei3
2022-06-10
Source PublicationOPTIMIZATION
ISSN0233-1934
Pages32
AbstractOptimization problems with least constraint violation have many important practical backgrounds. The related works in the literature normally focus on the norm square measure function and the classical augmented Lagrangian method is proved to be suitable for finding an approximate solution. This paper considers the constrained convex optimization problem with the least constraint violation under a general measure function. The properties of the conjugate dual associated with the measure function of the shifted problem are discussed through the relations between the dual function and the optimal value function. The differentiability of the dual function associated with the measure function is proved. The properties of augmented Lagrangian method induced by the measure function are characterized in terms of the dual function. The optimality conditions for the problem with the least constraint violation are established in term of the augmented Lagrangian. It is shown that the augmented Lagrangian method has the properties that the sequence of shift measure values is decreasing, the sequence of multipliers is unbounded, and the sequence of shifts converges to the least violated shift under an extra assumption.
KeywordConvex optimization measure function least constraint violation augmented Lagrangian method shifted problem
DOI10.1080/02331934.2022.2086055
Indexed BySCI
Language英语
Funding ProjectNatural Science Foundation of China[12021001] ; Natural Science Foundation of China[11991020] ; Natural Science Foundation of China[11991021] ; Natural Science Foundation of China[11971372] ; Natural Science Foundation of China[11971089] ; Natural Science Foundation of China[11731013] ; National Key R&D Program of China[2021YFA1000300] ; National Key R&D Program of China[2021YFA1000301] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA27000000] ; Dalian High-level Talent Innovation Project[2020RD09]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000810406500001
PublisherTAYLOR & FRANCIS LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61566
Collection计算数学与科学工程计算研究所
Corresponding AuthorZhang, Liwei
Affiliation1.Chinese Acad Sci, AMSS, ICMSEC, LSEC, Beijing, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
3.Dalian Univ Technol, Sch Math Sci, Dalian, Peoples R China
Recommended Citation
GB/T 7714
Dai, Yu-Hong,Zhang, Liwei. Study on convex optimization with least constraint violation under a general measure[J]. OPTIMIZATION,2022:32.
APA Dai, Yu-Hong,&Zhang, Liwei.(2022).Study on convex optimization with least constraint violation under a general measure.OPTIMIZATION,32.
MLA Dai, Yu-Hong,et al."Study on convex optimization with least constraint violation under a general measure".OPTIMIZATION (2022):32.
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