高阶张量Pareto-特征值的估计

Estimations of Pareto-eigenvalues for Higher-order Tensors

张量特征值互补问题有许多实际应用,它与一类高次齐次多项式优化关系密切,而后者是NP-难问题。给出了高阶张量Pareto-特征值的若干估计性质,并证明了对称的强-M-张量及单调张量的Pareto-特征值均为正。

Eigenvalue complementarity problems of tensors have many practical applications, and have closely connection with high order homogeneous polynomial optimization which is NP-hard.In this paper,some estimation proprieties of Pareto-eigenvalues of high order tensors are studied.We also prove that all the Pareto-eigenvalues of symmetric strong M-tensor and monotone tensor are positive.