A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors

摘要

In this paper, we consider solving the tensor complementarity problem (TCP). We first introduce the concept of the implicit Z-tensor, which is a generalization of Z-tensor. Then, based on a new fixed point reformulation of the TCP, we design an iterative algorithm for solving the TCP with an implicit Z-tensor under the assumption that the feasible set of the problem involved is nonempty. We prove that the proposed fixed point iterative method converges monotonically downward to a solution of the TCP. Furthermore, we establish the global linear rate of convergence of the proposed method under some reasonable assumptions. Compared with the existing related studies, the proposed method not only solves a wider range of TCPs, but also has a lower computational cost. The numerical results verify our theoretical findings.