Abstract
In this paper, finding the \(\mathcal {B}\)-eigenvalues of a symmetric tensor is equivalent to solving a least-square optimization problem. Based on the subspace technique, a trust region algorithm is presented. In trust region subproblem, the modified Broyden–Fletcher–Goldfarb–Shanno formula is adopted to generate the approximated matrices. In order to reduce the computation cost in each iteration, the quadratic subproblem is constructed in a subspace with lower dimension. Theoretic analysis of the given algorithm and convergence properties of the optimal solutions are established. Numerical results show that this method is efficient.
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Acknowledgements
We would like to thank the anonymous referees and the editor for their valuable comments. This work is supported by National Natural Science Foundation of China (11601473), the Innovation Talent Training Program of Science and Technology of Jilin Province of China (20180519011JH), the Science and Technology Development Project Program of Jilin Province (20190303132SF), the Applied Basic Research Programs of Science and Technology Department of Yunnan Province (2018FB001), Program for Excellent Young Talents of Yunnan University, Yunnan Provincial Ten Thousands Plan Young Top Talents, the Doctor Research Startup Project of Beihua University (170220014).
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Communicated by Anil Aswani.
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Cao, M., Huang, Q., Li, C. et al. A Subspace Modified Broyden–Fletcher–Goldfarb–Shanno Method for \(\mathcal {B}\)-eigenvalues of Symmetric Tensors. J Optim Theory Appl 184, 419–432 (2020). https://doi.org/10.1007/s10957-019-01617-5
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DOI: https://doi.org/10.1007/s10957-019-01617-5
Keywords
- Symmetric tensors
- \(\mathcal {B}\)-eigenvalues
- Modified Broyden–Fletcher–Goldfarb–Shanno
- Subspace technique
- Global convergence