On some properties of set-valued tensor complementarity problem

Abstract

In this paper, we introduce set-valued tensor complementarity problem where the elements of the involved tensors are defined based on a set-valued mapping. We study several properties of the solution set under the framework of set-valued mapping. We provide the necessary and sufficient conditions for the zero solution of a set-valued tensor complementarity problem. We introduce limit $R_0$-property for the set of tensors and establish a connection between limit $R_0$-property and the level boundedness of the merit function of the corresponding set-valued tensor complementarity problem.