Higher-degree eigenvalue complementarity problems for tensors

Chen Ling, Hongjin He, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)149-176
Number of pages28
JournalComputational Optimization and Applications
Volume64
Issue number1
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Alternating direction method of multipliers
  • Augmented Lagrangian method
  • Eigenvalue complementarity problem
  • Higher-degree cone eigenvalue
  • Polynomial optimization problem
  • Tensor

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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