A Lower Dimensional Linear Equation Approach to The M-Tensor Complementarity Problem

TL;DR

This paper introduces a novel lower dimensional linear equation method for solving the M-tensor complementarity problem, demonstrating convergence and efficiency through theoretical analysis and numerical experiments.

Contribution

It proposes a new iterative approach that reduces the problem to lower dimensional linear systems, with proven convergence properties and practical effectiveness.

Findings

Method converges monotonically to a solution.

Coefficient matrices become constant after finitely many iterations.

Numerical results support the method's efficiency.

Abstract

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each iteration, only a lower dimensional system of linear equation needs to be solved. The coefficient matrices of the lower dimensional linear systems are independent of the iteration after finitely many iterations. We show that starting from zero or some nonnegative point, the method generates a sequence of iterates that converges to a solution of the problem monotonically. We then make an improvement to the method and establish its monotone convergence. At last, we do numerical experiments to test the proposed methods. The results positively support the proposed methods.