Global Optimization of Polynomials over Real Algebraic Sets | |
Wang Chu1; Yang Zhi-Hong2,3; Zhi Lihong2,3 | |
刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY |
2019-02-01 | |
卷号 | 32期号:1页码:158-184 |
关键词 | Polynomial optimization real algebraic set generalized critical value |
ISSN号 | 1009-6124 |
DOI | 10.1007/s11424-019-8351-5 |
英文摘要 | Let f, g(1),..., g(s) be polynomials in R[X-1,..., X-n]. Based on topological properties of generalized critical values, the authors propose a method to compute the global infimum f* of f over an arbitrary given real algebraic set V = {x R-n | g(1)(x) = 0,..., g(s)(x) = 0}, where V is not required to be compact or smooth. The authors also generalize this method to solve the problem of optimizing f over a basic closed semi-algebraic set S = {x R-n | g(1)(x) 0,..., g(s)(x) 0}. |
资助项目 | National Key Research Project of China[2018YFA0306702] ; National Natural Science Foundation of China[11571350] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SPRINGER HEIDELBERG |
WOS记录号 | WOS:000458795500010 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32667] |
专题 | 系统科学研究所 |
通讯作者 | Wang Chu |
作者单位 | 1.Beijing Jinghang Computat & Commun Res Inst, Beijing 100074, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Wang Chu,Yang Zhi-Hong,Zhi Lihong. Global Optimization of Polynomials over Real Algebraic Sets[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2019,32(1):158-184. |
APA | Wang Chu,Yang Zhi-Hong,&Zhi Lihong.(2019).Global Optimization of Polynomials over Real Algebraic Sets.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,32(1),158-184. |
MLA | Wang Chu,et al."Global Optimization of Polynomials over Real Algebraic Sets".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 32.1(2019):158-184. |
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