The projected splitting iterative methods based on tensor splitting and its majorization matrix splitting for the tensor complementarity problem

Abstract

In this paper, we develop two kinds of the projected iterative methods for the tensor complementarity problem combining two different splitting frameworks. The first method is on the basis of tensor splitting, and its monotone convergence is proved based on the \({\mathcal{L}}\)-tensor and the strongly monotone tensor. Meanwhile, an alternative method is in the light of majorization matrix splitting, the convergence of which is given and is particularly analyzed based on the power Lipschitz tensor. Some numerical examples are tested to illustrate the proposed methods.