Study on convex optimization with least constraint violation under a general measure

doi:10.1080/02331934.2022.2086055

	Study on convex optimization with least constraint violation under a general measure
	Dai, Yu-Hong1,2 ; Zhang, Liwei 3
	2022-06-10
发表期刊	OPTIMIZATION
ISSN	0233-1934
页码	32
摘要	Optimization 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.
关键词	Convex optimization measure function least constraint violation augmented Lagrangian method shifted problem
DOI	10.1080/02331934.2022.2086055
收录类别	SCI
语种	英语
资助项目	Natural 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研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000810406500001
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61566
专题	计算数学与科学工程计算研究所
通讯作者	Zhang, Liwei
作者单位	1.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
推荐引用方式 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.