Higher-degree eigenvalue complementarity problems for tensors

Chen Ling (), Hongjin He () and Liqun Qi ()
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Chen Ling: Hangzhou Dianzi University
Hongjin He: Hangzhou Dianzi University
Liqun Qi: The Hong Kong Polytechnic University

Computational Optimization and Applications, 2016, vol. 64, issue 1, No 6, 149-176

Abstract: 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.

Keywords: Tensor; Higher-degree cone eigenvalue; Eigenvalue complementarity problem; Polynomial optimization problem; Augmented Lagrangian method; Alternating direction method of multipliers; 15A18; 15A69; 65K15; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10589-015-9805-x

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