Narrow Results

Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being $R_0$-tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.