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A Class of Second-Order Cone Eigenvalue Complementarity Problems for Higher-Order Tensors

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Abstract

In this paper, we consider the second-order cone tensor eigenvalue complementarity problem (SOCTEiCP) and present three different reformulations to the model under consideration. Specifically, for the general SOCTEiCP, we first show its equivalence to a particular variational inequality under reasonable conditions. A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the problem. Then, for the symmetric and sub-symmetric SOCTEiCPs, we reformulate them as appropriate nonlinear programming problems, which are extremely beneficial for designing reliable solvers to find solutions of the considered problem. Finally, we report some preliminary numerical results to verify our theoretical results.

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Acknowledgments

The authors would like to thank the two anonymous referees for their careful reading and valuable comments, which help us improve the presentation of this paper greatly.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Jiao-Jiao Hou, Chen Ling & Hong-Jin He

Authors
  1. Jiao-Jiao Hou
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  2. Chen Ling
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  3. Hong-Jin He
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Corresponding author

Correspondence to Hong-Jin He.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11171083, 11301123, and 11571087) and the Natural Science Foundation of Zhejiang Province (Nos. LZ14A010003 and LY17A010028).

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Hou, JJ., Ling, C. & He, HJ. A Class of Second-Order Cone Eigenvalue Complementarity Problems for Higher-Order Tensors. J. Oper. Res. Soc. China 5, 45–64 (2017). https://doi.org/10.1007/s40305-016-0137-z

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