A self-adaptive trust region method for extreme \(\mathcal {B}\)-eigenvalues of symmetric tensors

  • Mingyuan Cao
  • Qingdao Huang
  • Yueting Yang
Original Paper


A self-adaptive trust region method is presented for finding the largest or smallest \(\mathcal {B}\)-eigenvalues of symmetric tensors. One of the important features of this method is that \(\mathcal {B}\)-eigenvalues problem of symmetric tensors is transformed into a homogenous polynomial optimization. Global convergence of the proposed algorithm and second-order necessary conditions of the optimal solutions are established, respectively. Numerical experiments are listed to illustrate the efficiency of the proposed method.


Symmetric tensors Eigenvalues of tensors Polynomial optimization Trust region method Global convergence 

Mathematics Subject Classification (2010)

15A18 15A69 90C55 


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Funding information

This work is supported by the National Natural Science Foundation of China (11171131 and 11171003). Innovation Talent Training Program of Science and Technology of Jilin Province of China (20180519011JH).

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of MathematicsJilin UniversityChangchunChina
  2. 2.College of Mathematics and StatisticsBeihua UniversityJilinChina

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