Tensor Complementarity Problems—Part III: Applications

  • Zheng-Hai Huang
  • Liqun QiEmail author
Invited Paper


We have reviewed some theoretical and algorithmic developments for tensor complementarity problems and related models in the first part and the second part of this paper, respectively. In this part, we present a survey for some applications of tensor complementarity problems and polynomial complementarity problems. We first describe some equivalent classes of tensor complementarity problems and polynomial complementarity problems, since many practical problems can be modeled as forms of those equivalent problems; and then, we review three practical applications of tensor complementarity problems and polynomial complementarity problems. The first practical application is about a class of multi-person noncooperative games, which is modeled as a tensor complementarity problem, and particularly, an explicit relationship between the solutions to these two classes of problems is presented. The second practical problem is about the hypergraph clustering problem, which can be solved by a tensor complementarity problem. The third practical problem is about a class of traffic equilibrium problems, which is modeled as a polynomial complementarity problem. Some further issues are given.


Tensor complementarity problem Multi-person noncooperation game Hypergraph clustering Static traffic equilibrium problem 

Mathematics Subject Classification

90C33 90C30 65H10 



We are very grateful to professors Chen Ling, Yisheng Song, Shenglong Hu, and Ziyan Luo for reading the first draft of this paper and putting forward valuable suggestions for revision. The first author’s work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11431002 and 11871051), and the second author’s work is partially supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 15302114, 15300715, 15301716, and 15300717).


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Authors and Affiliations

  1. 1.School of MathematicsTianjin UniversityTianjinPeople’s Republic of China
  2. 2.Department of Mathematics, School of ScienceHangzhou Dianzi UniversityHangzhouPeople’s Republic of China
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong

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