KMS Of Academy of mathematics and systems sciences, CAS
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 | |
发表期刊 | PACIFIC JOURNAL OF OPTIMIZATION |
ISSN | 1348-9151 |
卷号 | 11期号:2页码:291-307 |
摘要 | It 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. |
关键词 | symmetric tensor extreme Z-eigenvalue feasible trust-region global convergence local quadratic convergence |
语种 | 英语 |
资助项目 | Chinese 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研究方向 | Operations Research & Management Science ; Mathematics |
WOS类目 | Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000355241700006 |
出版者 | YOKOHAMA PUBL |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/19849 |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Hao, Chun-Lin |
作者单位 | 1.Beijing Univ Technol, Sch Appl Math, Beijing, Peoples R China 2.Acad Math & Syst Sci, Beijing 100190, Peoples R China |
推荐引用方式 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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