Higher-degree eigenvalue complementarity problems for tensors

Chen Ling; Hongjin He; Liqun Qi

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arXiv · 1507.03412

Higher-degree eigenvalue complementarity problems for tensors

Chen Ling·Hongjin He·Liqun Qi

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Abstract

In this paper, we introduce a unified framework of Tensor Higher-Degree Eigenvalue Complementarity Problem (THDEiCP), which goes beyond the framework of the typical Quadratic Eigenvalue Complementarity Problem (QEiCP) for matrices. First, we study some topological properties of higher-degree cone eigenvalues of tensors. Based upon the symmetry assumptions on the underlying tensors, we then reformulate THDEiCP as a weakly coupled homogeneous polynomial optimization problem, which might be greatly helpful for designing implementable algorithms to solve the problem under consideration numerically. As more general theoretical results, we present the results concerning existence of solutions of THDEiCP without symmetry conditions. Finally, we propose an easily implementable algorithm to solve THDEiCP, and report some computational results.

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BibTeX RIS

Chen Ling, Hongjin He, Liqun Qi. 2015-07-13. Higher-degree eigenvalue complementarity problems for tensors. https://arxiv.org/abs/1507.03412

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