Tensor Complementarity Problems—Part III: Applications

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.