Global Optimization of Polynomials over Real Algebraic Sets

doi:10.1007/s11424-019-8351-5

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	Global Optimization of Polynomials over Real Algebraic Sets
	Wang Chu 1; Yang Zhi-Hong 2,3; Zhi Lihong2,3
	2019-02-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	32 期号:1 页码:158-184
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}.
关键词	Polynomial optimization real algebraic set generalized critical value
DOI	10.1007/s11424-019-8351-5
语种	英语
资助项目	National Key Research Project of China[2018YFA0306702] ; National Natural Science Foundation of China[11571350]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000458795500010
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32668
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.