Locally Optimal Eigenpairs of Orthogonally Decomposable Tensors: A Generalized Proof

Lei Wang (), Xiurui Geng () and Lei Zhang ()
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Lei Wang: Chongqing University
Xiurui Geng: Chinese Academy of Sciences
Lei Zhang: Chongqing University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 8, 199-220

Abstract: 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.

Keywords: E-eigenpairs; Orthogonally decomposable; Symmetric tensors; Projected Hessian matrix; Local optimality; Constrained optimization; 15A69; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02390-w

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