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作者:

Hao, Chun-Lin (Hao, Chun-Lin.) | Cui, Chun-Feng (Cui, Chun-Feng.) | Dai, Yu-Hong (Dai, Yu-Hong.)

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SCIE

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:

feasible trust-region global convergence extreme Z-eigenvalue symmetric tensor local quadratic convergence

作者机构:

  • [ 1 ] [Hao, Chun-Lin]Beijing Univ Technol, Sch Appl Math, Beijing, Peoples R China
  • [ 2 ] [Cui, Chun-Feng]Acad Math & Syst Sci, Beijing 100190, Peoples R China
  • [ 3 ] [Dai, Yu-Hong]Acad Math & Syst Sci, Beijing 100190, Peoples R China

通讯作者信息:

  • [Hao, Chun-Lin]Beijing Univ Technol, Sch Appl Math, Pingleyuan 100, Beijing, Peoples R China

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来源 :

PACIFIC JOURNAL OF OPTIMIZATION

ISSN: 1348-9151

年份: 2015

期: 2

卷: 11

页码: 291-307

0 . 2 0 0

JCR@2022

ESI学科: ENGINEERING;

ESI高被引阀值:174

JCR分区:4

中科院分区:4

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