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.

中文翻译：

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张量互补问题的基于张量分裂及其主化矩阵分裂的投影分裂迭代方法

在本文中，我们结合两种不同的分裂框架，开发了两种用于张量互补问题的投影迭代方法。第一种方法是基于张量分裂的，并基于\({\mathcal{L}}\)张量和强单调张量证明了其单调收敛性。同时，另一种方法是针对主化矩阵分裂，给出了其收敛性，并基于功率Lipschitz张量对其收敛性进行了具体分析。测试了一些数值例子来说明所提出的方法。