Abstract
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.
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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).
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Cao, M., Huang, Q. & Yang, Y. A self-adaptive trust region method for extreme \(\mathcal {B}\)-eigenvalues of symmetric tensors. Numer Algor 81, 407–420 (2019). https://doi.org/10.1007/s11075-018-0554-7
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DOI: https://doi.org/10.1007/s11075-018-0554-7