On the lower and upper bounds of the solution set of the tensor complementarity problem

The tensor complementarity problem (TCP) is to find a vector x∈Rn such that x≥0,q+Axm−1≥0,x⊤(Axm−1+q)=0 with A∈R[m,n] and q∈Rn. In this paper, we further investigate the lower and upper bounds of the solution set of the tensor complementarity problem with q∈R+n. In addition, new quantities are introduced to present tighter upper bounds of the solution set of the TCP(A,q) when A is a strictly semi-positive tensor or an R0-tensor. Numerical examples are given to show the efficiency of the proposed results.