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Volume 39, Issue 3
An Adaptive Trust-Region Method for Generalized Eigenvalues of Symmetric Tensors

Yuting Chen, Mingyuan Cao, Yueting Yang & Qingdao Huang

DOI: 10.4208/jcm.2001-m2019-0017

J. Comp. Math., 39 (2021), pp. 358-374.

Published online: 2021-04

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  • Abstract

For symmetric tensors, computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere. In this paper, we present an adaptive trust-region 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.

  • Keywords

Symmetric tensors, Generalized eigenvalues, Trust-region, Global convergence, Local quadratic convergence.

  • AMS Subject Headings

15A18, 15A69, 90C55.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

caomingyuan0918@163.com (Mingyuan Cao)

yyt2858@163.com (Yueting Yang)

huangqd@jlu.edu.cn (Qingdao Huang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-358, author = {Chen , YutingCao , MingyuanYang , Yueting and Huang , Qingdao}, title = {An Adaptive Trust-Region Method for Generalized Eigenvalues of Symmetric Tensors}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {3}, pages = {358--374}, abstract = {

For symmetric tensors, computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere. In this paper, we present an adaptive trust-region 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2001-m2019-0017}, url = {http://global-sci.org/intro/article_detail/jcm/18744.html} }
TY - JOUR T1 - An Adaptive Trust-Region Method for Generalized Eigenvalues of Symmetric Tensors AU - Chen , Yuting AU - Cao , Mingyuan AU - Yang , Yueting AU - Huang , Qingdao JO - Journal of Computational Mathematics VL - 3 SP - 358 EP - 374 PY - 2021 DA - 2021/04 SN - 39 DO - http://doi.org/10.4208/jcm.2001-m2019-0017 UR - https://global-sci.org/intro/article_detail/jcm/18744.html KW - Symmetric tensors, Generalized eigenvalues, Trust-region, Global convergence, Local quadratic convergence. AB -

For symmetric tensors, computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere. In this paper, we present an adaptive trust-region 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.

Chen , YutingCao , MingyuanYang , Yueting and Huang , Qingdao. (2021). An Adaptive Trust-Region Method for Generalized Eigenvalues of Symmetric Tensors. Journal of Computational Mathematics. 39 (3). 358-374. doi:10.4208/jcm.2001-m2019-0017
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