KMS Of Academy of mathematics and systems sciences, CAS
| Sufficient conditions for existence of global minimizers of functions on Hilbert spaces | |
| Chen, Liang1; Dai, Yu-Hong2,3; Wei, Zhou4,5 | |
| 2022-02-14 | |
| Source Publication | JOURNAL OF GLOBAL OPTIMIZATION
 |
| ISSN | 0925-5001 |
| Pages | 11 |
| Abstract | 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. |
| Keyword | Sufficient condition Global minmizer Primal-lower-nice Subdifferential evolution problem Palais-Smale condition |
| DOI | 10.1007/s10898-022-01133-3 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000754491000001 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60048 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wei, Zhou |
| Affiliation | 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 |
| Recommended Citation 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. |
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