Linearized Methods for Tensor Complementarity Problems

In this paper, we first propose a linearized method for solving the tensor complementarity problem. The subproblems of the method can be solved by solving linear complementarity problems with a constant matrix. We show that if the initial point is appropriately chosen, then the generated sequence of iterates converges to a solution of the problem monotonically. We then propose a lower-dimensional equation method and establish its monotone convergence. The subproblems of the method are lower-dimensional systems of linear equations. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods.