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 - <p style="text-align: justify;">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.</p>