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	A note on semidefinite programming relaxations for polynomial optimization over a single sphere
	Hu Jiang1; Jiang Bo2; Liu Xin3; Wen ZaiWen1
	2016-08
关键词	polynomial optimization over a single sphere semidefinite programming best rank-1 tensor approximation Bose-Einstein condensates
卷号	59
期号	8
DOI	10.1007/s11425-016-0301-5
页码	1543-1560
英文摘要	We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates (BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.
会议录出版者	SCIENCE PRESS
会议录出版地	16 DONGHUANGCHENGGEN NORTH ST, BEIJING 100717, PEOPLES R CHINA
语种	英语
WOS研究方向	Mathematics
WOS记录号	WOS:000380212100007
内容类型	会议论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/3361]
专题	上海财经大学
作者单位	1.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China; 2.Shanghai Univ Finance & Econ, Sch Informat Management & Engn, Res Ctr Management Sci & Data Analyt, Shanghai 200433, Peoples R China; 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu Jiang,Jiang Bo,Liu Xin,et al. A note on semidefinite programming relaxations for polynomial optimization over a single sphere[C]. 见:.

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