AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS

doi:10.4208/jcm.2001-m2019-0017

Journal of Computational Mathematics ›› 2021, Vol. 39 ›› Issue (3): 358-374.DOI: 10.4208/jcm.2001-m2019-0017

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AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS

Yuting Chen¹, Mingyuan Cao², Yueting Yang², Qingdao Huang³

1. School of Mathematics, Jilin University, Changchun 130012, China;
2. School of Mathematics and Statistics, Beihua University, Jilin 132013, China;
3. School of Mathematics, Jilin University, Changchun 130012, China

Received:2019-01-29 Revised:2019-01-29 Online:2021-05-15 Published:2021-04-12
Contact: Qingdao Huang,Email:huangqd@jlu.edu.cn
Supported by:
The research of Yueting Yang is supported in part by the NNSF of China (11171003), the Innovation Talent Training Program of Science and Technology of Jilin Province of China (20180519011JH) and the Science and Technology Development Project Program of Jilin Province (20190303132SF). The research of Mingyuan Cao is partially supported by the Project of Education Department of Jilin Province (JJKH20200028KJ). The research of Qingdao Huang is partially supported by the NNSF of China (11171131).

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Yuting Chen, Mingyuan Cao, Yueting Yang, Qingdao Huang. AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS[J]. Journal of Computational Mathematics, 2021, 39(3): 358-374.

For symmetric tensors, computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere. In this paper, we present an adaptive trustregion method for generalized eigenvalues of symmetric tensors. One of the features is that the trust-region radius is automatically updated by the adaptive technique to improve the algorithm performance. The other one is that a projection scheme is used to ensure the feasibility of all iteratives. Global convergence and local quadratic convergence of our algorithm are established, respectively. The preliminary numerical results show the efficiency of the proposed algorithm.

Key words: Symmetric tensors, Generalized eigenvalues, Trust-region, Global convergence, Local quadratic convergence

CLC Number:

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AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS

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