Connectedness of the solution set of the tensor complementarity problem

Abstract In this paper, we investigate the connectedness of the solution set of the tensor complementarity problem (TCP). By exploring the structure of underlying tensor in the TCP, we establish two results. The first is that if the solution set of the TCP is connected, then the underlying tensor must be semi-positive. The other is that the solution set of the TCP is connected under a newly proposed condition. The proposed condition is a tensor extension for the linear complementarity problem, and the result improves a direct adoption of the result for general nonlinear complementarity problem. Some examples are given which confirm our theoretical findings.