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Homogenization for polynomial optimization with unbounded sets

文献类型：期刊论文

作者Huang, Lei1,2; Nie, Jiawang3; Yuan, Ya-Xiang1
刊名MATHEMATICAL PROGRAMMING
出版日期2022-08-20
页码41
关键词Polynomial optimization Homogenization Moment-SOS relaxations Optimality conditions
ISSN号0025-5610
DOI10.1007/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
WOS记录号WOS:000842139200002
出版者SPRINGER HEIDELBERG
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.

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来源：数学与系统科学研究院

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