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

文献类型：期刊论文

作者Dai, Yu-Hong2,3; Zhang, Liwei1
刊名OPTIMIZATION
出版日期2022-06-10
页码32
关键词Convex optimization measure function least constraint violation augmented Lagrangian method shifted problem
ISSN号0233-1934
DOI10.1080/02331934.2022.2086055
英文摘要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.
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
语种英语
WOS记录号WOS:000810406500001
出版者TAYLOR & FRANCIS LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/61565]  
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.Dalian Univ Technol, Sch Math Sci, Dalian, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
3.Chinese Acad Sci, AMSS, ICMSEC, LSEC, Beijing, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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