In this paper, we first propose a linearized method for solving the tensor complementarity problem. The subproblems of the method can be solved by solving linear complementarity problems with a constant matrix. We show that if the initial point is appropriately chosen, then the generated sequence of iterates converges to a solution of the problem monotonically. We then propose a lower-dimensional equation method and establish its monotone convergence. The subproblems of the method are lower-dimensional systems of linear equations. At last, we do numerical experiments to test the proposed methods. The results show the efficiency of the proposed methods.

中文翻译：

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张量互补问题的线性化方法

在本文中，我们首先提出了一种解决张量互补问题的线性化方法。该方法的子问题可以通过用常数矩阵求解线性互补问题来求解。我们表明，如果初始点被适当地选择，那么生成的迭代序列会单调收敛到问题的解决方案。然后我们提出了一种低维方程方法并建立了它的单调收敛性。该方法的子问题是线性方程的低维系统。最后，我们进行了数值实验来测试所提出的方法。结果表明了所提出方法的有效性。