A linearized method for solving tensor complementarity problems with implicit Z -tensors

In this paper, some properties of implicit Z -tensors are studied, and it is proved that an implicit Z -tensor is a nonsingular implicit M -tensor if and only if it is semi-positive. Then, a linearized method to solve tensor complementarity problem with an implicit Z -tensor is presented. Under the condition that the feasible set is nonempty, it is proved that the iterative sequence generated by the the method is monotonic convergence, which weakens the convergence condition of the related method in the literature. Final numerical experiments demonstrate the effectiveness of the method.