Sufficient conditions for existence of global minimizers of functions on Hilbert spaces

doi:10.1007/s10898-022-01133-3

CSpace

	Sufficient conditions for existence of global minimizers of functions on Hilbert spaces
	Chen, Liang 1; Dai, Yu-Hong 2,3; Wei, Zhou 4,5
	2022-02-14
发表期刊	JOURNAL OF GLOBAL OPTIMIZATION
ISSN	0925-5001
页码	11
摘要	Given an objective function (differentiable or nondifferentiable), an important optimization problem is to find the global minimizer of the given function and a natural issue is to identify such functions with the global property. In this paper, we study real-valued functions defined on a Hilbert space and provide several sufficient conditions to ensure the existence of the global minimizer of such functions. For a proper lower semicontinuous function, we prove that a global minimizer can be guaranteed if it is bounded below, has the primal-lower-nice property and satisfies the generalized Palais-Smale condition. This result can cover the classic differentiable case whose proof depends heavily on the global existence of the ordinary differential equation. Several examples are constructed to show that the global minimizer may be violated if any of three conditions above is dropped.
关键词	Sufficient condition Global minmizer Primal-lower-nice Subdifferential evolution problem Palais-Smale condition
DOI	10.1007/s10898-022-01133-3
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundations of China[11991021] ; National Natural Science Foundations of China[12021001] ; National Natural Science Foundations of China[11971422] ; National Natural Science Foundations of China[11826204] ; National Natural Science Foundations of China[11826206] ; CAS Light of West China Program ; Jointed Key Project of Yunnan Provincial Science and Technology Department and Yunnan University[2018FY001014] ; Program for Innovative Research Team (in Science and Technology) in Universities of Yunnan Province[C176240111009]
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000754491000001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60048
专题	中国科学院数学与系统科学研究院
通讯作者	Wei, Zhou
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China 5.Yunnan Univ, Dept Math, Kunming 650091, Yunnan, Peoples R China
推荐引用方式 GB/T 7714	Chen, Liang,Dai, Yu-Hong,Wei, Zhou. Sufficient conditions for existence of global minimizers of functions on Hilbert spaces[J]. JOURNAL OF GLOBAL OPTIMIZATION,2022:11.
APA	Chen, Liang,Dai, Yu-Hong,&Wei, Zhou.(2022).Sufficient conditions for existence of global minimizers of functions on Hilbert spaces.JOURNAL OF GLOBAL OPTIMIZATION,11.
MLA	Chen, Liang,et al."Sufficient conditions for existence of global minimizers of functions on Hilbert spaces".JOURNAL OF GLOBAL OPTIMIZATION (2022):11.