  In this paper, we establish a new approach to solve the tensor
complementarity problem (TCP). A mixed integer programming model is given and
the TCP is solved by solving the model. The TCP is shown to be formulated as an
equivalent mixed integer feasibility problem. Based on the reformulation, some
conditions are obtained to guarantee the solvability of the TCP. Specially, a
sufficient condition is given for TCP without solutions. A necessary and
sufficient condition is given for existence of solutions. We also give a
concrete bound for the solution set of the TCP with positive definite tensors.
Moreover, we show that the TCP with a diagonal positive definite tensor has a
unique solution. Numerical experiments on several test problems illustrate the
efficiency of the proposed approach in terms of the quality of the obtained
solutions.
