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.

正交可分解 (odeco) 张量是一类特殊的对称张量。以往的工作主要集中于研究其E特征对问题，并在E特征对的数量和局部最优性方面取得了一些理论成果。然而，关于每个特征对的局部最优性，现有工作仅分析三阶张量情况。在本文中，我们通过检查相关约束优化模型的二阶必要条件并推导局部最优识别的等效矩阵公式准则，进一步针对任何高阶张量利用这个问题。最后，给出了odeco张量特征对局部最优性的广义结论，并进行了一些模拟实验进行验证。