This paper studies tensor Z-eigenvalue complementarity problems. We formulate the tensor Z-eigenvalue complementarity problem as constrained polynomial optimization, and propose a semidefinite relaxation algorithm for solving the complementarity Z-eigenvalues of tensors. For every tensor that has finitely many complementarity Z-eigenvalues, we can compute all of them and show that our algorithm has the asymptotic and finite convergence. Numerical experiments indicate the efficiency of the proposed method.

中文翻译：

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张量Z特征值互补问题

本文研究了张量Z-特征值互补问题。我们将张量Z-特征值互补性公式化为约束多项式优化，并提出了一种半确定松弛算法来求解张量的Z-特征值互补性。对于具有有限多个互补Z-特征值的每个张量，我们可以对其进行计算，并证明我们的算法具有渐近和有限收敛性。数值实验表明了该方法的有效性。