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A FEASIBLE TRUST-REGION METHOD FOR CALCULATING EXTREME Z-EIGENVALUES OF SYMMETRIC TENSORS
Hao, Chun-Lin1; Cui, Chun-Feng2; Dai, Yu-Hong2
2015-04-01
Source PublicationPACIFIC JOURNAL OF OPTIMIZATION
ISSN1348-9151
Volume11Issue:2Pages:291-307
AbstractIt is known that computing the largest (smallest) Z-eigenvalue of a symmetric tensor is equivalent to maximizing (minimizing) a homogenous polynomial over the unit sphere. Based on such a reformulation, we shall propose a feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors. One basic feature of the method is that the true Hessian, which is ready for polynomials, is utilized in the trust-region subproblem so that any cluster point of the iterations can be shown to satisfy the second-order necessary conditions. The other feature is that after a trial step d(k) is provided by solving the trust-region subproblem at the current point x(k), the projection of x(k) + d(k) to the unit sphere, instead of the point x(k) + d(k) itself, is judged and if successful, is used for the next point. Global convergence and local quadratic convergence of the feasible trust-region method are established for the tensor Z-eigenvalue problem. The preliminary numerical results over several testing problems show that the feasible trust-region method is quite promising.
Keywordsymmetric tensor extreme Z-eigenvalue feasible trust-region global convergence local quadratic convergence
Language英语
Funding ProjectChinese NSF[11301016] ; Chinese NSF[11331012] ; Chinese NSF[81173633] ; Research Fund for the Doctoral Program of Higher Education of China[20131103120029] ; Ri-Xin Talents Project of Beijing University of Technology ; National Key Basic Research Program of China[2015CB856000] ; China National Funds for Distinguished Young Scientists[11125107]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000355241700006
PublisherYOKOHAMA PUBL
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19849
Collection计算数学与科学工程计算研究所
Corresponding AuthorHao, Chun-Lin
Affiliation1.Beijing Univ Technol, Sch Appl Math, Beijing, Peoples R China
2.Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Hao, Chun-Lin,Cui, Chun-Feng,Dai, Yu-Hong. A FEASIBLE TRUST-REGION METHOD FOR CALCULATING EXTREME Z-EIGENVALUES OF SYMMETRIC TENSORS[J]. PACIFIC JOURNAL OF OPTIMIZATION,2015,11(2):291-307.
APA Hao, Chun-Lin,Cui, Chun-Feng,&Dai, Yu-Hong.(2015).A FEASIBLE TRUST-REGION METHOD FOR CALCULATING EXTREME Z-EIGENVALUES OF SYMMETRIC TENSORS.PACIFIC JOURNAL OF OPTIMIZATION,11(2),291-307.
MLA Hao, Chun-Lin,et al."A FEASIBLE TRUST-REGION METHOD FOR CALCULATING EXTREME Z-EIGENVALUES OF SYMMETRIC TENSORS".PACIFIC JOURNAL OF OPTIMIZATION 11.2(2015):291-307.
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