On the cone eigenvalue complementarity problem for higher-order tensors
On the cone eigenvalue complementarity problem for higher-order tensors
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DOI：
10.1007/s10589-015-9767-z
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发表时间：
2015-01
影响因子：
2.2
通讯作者：
C. Ling;Hongjin He;L. Qi
中科院分区：
文献类型：
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作者：
C. Ling;Hongjin He;L. Qi
本文考虑广义特征值互补问题(TGEiCP)，它是矩阵特征值互补问题(EiCP)的一个有趣的推广。首先，我们给出了一个肯定的结果，证明了TGEiCP是可解的，并且在一些合理的假设下至少有一个解。然后，我们引入了TGEiCP的两个优化重构式，从而有益地建立了张量的锥本征值的上界。此外，关于TGEiCP的特征值数的界的一些新结果进一步丰富了TGEiCP的理论。最后，针对所考虑的问题，提出了一种可实现的求解TGEiCP问题的投影算法。作为理论结果的说明，给出了初步的计算结果。
In this paper, we consider thetensor generalized eigenvalue complementarity problem(TGEiCP), which is an interesting generalization of matrixeigenvalue complementarity problem(EiCP). First, we give an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound on cone eigenvalues of tensors. Moreover, some new results concerning the bounds on the number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.