On a Class of Semi-Positive Tensors in Tensor Complementarity Problem

Recently, the tensor complementarity problem has been investigated in the literature. In this paper, we extend a class of structured matrices to higher-order tensors; the corresponding tensor complementarity problem has a unique solution for any nonzero nonnegative vector. We discuss their relationships with semi-positive tensors and strictly semi-positive tensors. We also study the property of such a structured tensor. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. We also give two equivalent formulations of such a structured tensor.