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Global Uniqueness and Solvability for Tensor Complementarity Problems

  • Xue-Li Bai
  • Zheng-Hai HuangEmail author
  • Yong Wang
Article

Abstract

Recently, the tensor complementarity problem has been investigated in the literature. An important question involving the property of global uniqueness and solvability for a class of tensor complementarity problems was proposed by Song and Qi (J Optim Theory Appl, 165:854–873, 2015). In the present paper, we give an answer to this question by constructing two counterexamples. We also show that the solution set of this class of tensor complementarity problems is nonempty and compact. In particular, we introduce a class of related structured tensors and show that the corresponding tensor complementarity problem has the property of global uniqueness and solvability.

Keywords

Tensor complementarity problem Nonlinear complementarity problem Global uniqueness and solvability P tensor Strong P tensor 

Mathematics Subject Classification

90C33 65K10 15A18 15A69 65F15 65F10 

Notes

Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11171252 and 11431002).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceTianjin UniversityTianjinPeople’s Republic of China
  2. 2.Center for Applied Mathematics of Tianjin UniversityTianjinPeople’s Republic of China

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