An equivalent tensor equation to the tensor complementarity problem with positive semi-definite Z-tensor

Abstract

We are concerned with the tensor complementarity problem with positive semi-definite Z-tensor. Under the assumption that the problem has a solution at which the strict complementarity holds, we show that the problem is equivalent to a system of lower dimensional tensor equations. It provides a way to get a solution of the complementarity problem via solving a system of lower dimensional tensor equations. The results obtained in the paper improve the existing results even for the linear complementarity problem. Our preliminary numerical results positively support the results of the paper.