Homogenization for polynomial optimization with unbounded sets

doi:10.1007/s10107-022-01878-5

CSpace

	Homogenization for polynomial optimization with unbounded sets
	Huang, Lei 1,2; Nie, Jiawang 3; Yuan, Ya-Xiang 1
	2022-08-20
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
页码	41
摘要	This paper considers polynomial optimization with unbounded sets. We give a homogenization formulation and propose a hierarchy of Moment-SOS relaxations to solve it. Under the assumptions that the feasible set is closed at infinity and the ideal of homogenized equality constraining polynomials is real radical, we show that this hierarchy of Moment-SOS relaxations has finite convergence, if some optimality conditions (i.e., the linear independence constraint qualification, strict complementarity and second order sufficient conditions) hold at every minimizer, including the one at infinity. Moreover, we prove extended versions of Putinar-Vasilescu type Positivstellensatz for polynomials that are nonnegative on unbounded sets. The classical Moment-SOS hierarchy with denominators is also studied. In particular, we give a positive answer to a conjecture of Mai, Lasserre and Magron in their recent work.
关键词	Polynomial optimization Homogenization Moment-SOS relaxations Optimality conditions
DOI	10.1007/s10107-022-01878-5
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12288201]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000842139200002
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/61109
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Lei
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Calif San Diego, Dept Math, 9500 Gilman Dr, La Jolla, CA 92093 USA
推荐引用方式 GB/T 7714	Huang, Lei,Nie, Jiawang,Yuan, Ya-Xiang. Homogenization for polynomial optimization with unbounded sets[J]. MATHEMATICAL PROGRAMMING,2022:41.
APA	Huang, Lei,Nie, Jiawang,&Yuan, Ya-Xiang.(2022).Homogenization for polynomial optimization with unbounded sets.MATHEMATICAL PROGRAMMING,41.
MLA	Huang, Lei,et al."Homogenization for polynomial optimization with unbounded sets".MATHEMATICAL PROGRAMMING (2022):41.