THREE CLASSES OF COPOSITIVE-TYPE TENSORS AND TENSOR COMPLEMENTARITY PROBLEMS

摘要

In the field of complementary problems, an important issue is to investigate under what conditions feasibility of the problem can lead to its solvability. For the linear complementarity problem, such an issue has been studied when the matrix involved is a copositive star matrix, a pseudomonotone matrix, or a copositive plus matrix. In this paper, we first introduce the concepts of copositive star tensors, pseudomonotone tensors, and copositive plus tensors, which are natural extensions of copositive star matrices, pseudomonotone matrices, and copositive plus matrices, respectively. We discuss the relationships among these three classes of tensors and give a complete characterization. Then we establish an existence result of solutions to the tensor complementarity problem under the assumption that the tensor involved is one of these three classes of tensors and an addition condition. Finally we show the equivalence of solvability and feasibility for the tensor complementarity problem with the tensor involved being one of these three classes of tensors.