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Journal of Global Optimization

, Volume 73, Issue 4, pp 789–800 | Cite as

A mixed integer programming approach to the tensor complementarity problem

  • Shouqiang Du
  • Liping ZhangEmail author
Article

Abstract

The tensor complementarity problem is a special instance of nonlinear complementarity problems, which has many applications. How to solve the tensor complementarity problem, via analyzing the structure of the related tensor, is one of very important research issues. In this paper, we propose a mixed integer programming approach for solving the tensor complementarity problem. We reformulate the tensor complementarity problem as an equivalent mixed integer feasibility problem. Based on the reformulation, some conditions for the solution existence and some solution properties of the tensor complementarity problem are given. We also prove that the tensor complementarity problem, corresponding to a positive definite diagonal tensor, has a unique solution. Finally, numerical results are reported to indicate the efficiency of the proposed algorithm.

Keywords

Tensor complementarity problem Mixed integer programming Unique solution Positive definite 

Mathematics Subject Classification

15A69 90C11 

Notes

Acknowledgements

The authors would like to thank the editor and the anonymous referees for their helpful constructive comments and suggestions which lead to a significantly improved version of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQingdao UniversityQingdaoChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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