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A mixed integer programming approach to the tensor complementarity problem

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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.

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Shouqiang Du

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Liping Zhang

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  1. Shouqiang Du
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  2. Liping Zhang
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Correspondence to Liping Zhang.

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This work was supported by the National Nature Science Foundation of China (Grant Nos. 11671220, 11771244) and the Nature Science Foundation of Shandong Province (ZR2016AM29).

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Du, S., Zhang, L. A mixed integer programming approach to the tensor complementarity problem. J Glob Optim 73, 789–800 (2019). https://doi.org/10.1007/s10898-018-00731-4

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  • DOI: https://doi.org/10.1007/s10898-018-00731-4

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