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On the cone eigenvalue complementarity problem for higher-order tensors

Chen Ling (macling***at***hdu.edu.cn)
Hongjin He (hehj2003***at***163.com)
Liqun Qi (maqilq***at***polyu.edu.hk)

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 given 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 of cone eigenvalues of tensors. Moreover, some new results concerning the bounds of 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.

Keywords: Higher order tensor, eigenvalue complementarity problem, cone eigenvalue, optimization reformulation, projection algorithm

Category 1: Complementarity and Variational Inequalities

Category 2: Global Optimization (Other )

Citation:

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Entry Submitted: 01/11/2015
Entry Accepted: 01/12/2015
Entry Last Modified: 01/30/2015

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