Solvability of monotone tensor complementarity problems

The tensor complementarity problem is a special instance in the class of nonlinear problems, which has many applications multi-person noncooperative games, hypergraph clustering problems and traffic equilibrium problems. Two most important research issues are how to identify solvability solve such via analyzing structure involved tensor. In this paper, based on concept monotone mappings, we introduce new structured tensors corresponding problem. We show that solution set nonempty compact under feasibility assumption. Moreover, necessary sufficient condition for ensuring given Based Huber function, propose regularized smoothing Newton method establish its global convergence. Under some mild assumptions, proposed algorithm superlinearly convergent. Preliminary numerical results indicate very promising.