On the cone eigenvalue complementarity problem for higher-order tensors

Chen Ling (), Hongjin He () and Liqun Qi ()

Computational Optimization and Applications, 2016, vol. 63, issue 1, 143-168

Abstract: In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue 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. Copyright Springer Science+Business Media New York 2016

Keywords: Higher order tensor; Eigenvalue complementarity problem; Cone eigenvalue; Optimization reformulation; Projection algorithm; 15A18; 15A69; 65K15; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10589-015-9767-z

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