Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/62347
Title: Higher-degree eigenvalue complementarity problems for tensors
Authors: Ling, C
He, H
Qi, LQ 
Keywords: Tensor
Higher-degree cone eigenvalue
Eigenvalue complementarity problem
Polynomial optimization problem
Augmented Lagrangian method
Alternating direction method of multipliers
Issue Date: 2016
Publisher: Springer
Source: Computational optimization and applications, 2016, v. 64, no. 1, p. 149-176 How to cite?
Journal: Computational optimization and applications 
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 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.
URI: http://hdl.handle.net/10397/62347
ISSN: 0926-6003
EISSN: 1573-2894
DOI: 10.1007/s10589-015-9805-x
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