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- Title
Locally Optimal Eigenpairs of Orthogonally Decomposable Tensors: A Generalized Proof.
- Authors
Wang, Lei; Geng, Xiurui; Zhang, Lei
- Abstract
Orthogonally decomposable (odeco) tensors is a special class of symmetric tensors. Previous works have focused on investigating its E-eigenpairs problem, and made some theoretical achievements concerning the number and the local optimality of E-eigenpairs. However, concerning local optimality of each eigenpair, the existing work only analyzed the third-order tensor case. In this paper, we further exploit this issue for any higher-order tensors by checking second-order necessary condition of the related constrained optimization model and deducing an equivalent matrix formula criterion for local optimality identification. Finally, a generalized conclusion for local optimality of eigenpairs for odeco tensors is provided, and some simulated experiments are conducted for validation.
- Subjects
CONSTRAINED optimization; HESSIAN matrices
- Publication
Journal of Optimization Theory & Applications, 2024, Vol 201, Issue 1, p199
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-024-02390-w