Homogenization for polynomial optimization with unbounded sets

doi:10.1007/s10107-022-01878-5

	Homogenization for polynomial optimization with unbounded sets
	Huang, Lei 1,2; Nie, Jiawang 3; Yuan, Ya-Xiang 1
刊名	MATHEMATICAL PROGRAMMING
	2022-08-20
页码	41
关键词	Polynomial optimization Homogenization Moment-SOS relaxations Optimality conditions
ISSN号	0025-5610
DOI	10.1007/s10107-022-01878-5
英文摘要	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.
资助项目	National Natural Science Foundation of China[12288201]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000842139200002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61108]
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.