New Pareto Z-eigenvalue localization theorems for tensors with applications

Abstract: In this paper, we establish some new localization sets for Pareto Z-eigenvalues of tensor eigenvalue complementarity problems and discuss the relationships among existing ones. As applications, a sufficient condition for the solution existence of the tensor complementarity problem (TCP) and the tensor generalized eigenvalue complementarity problem (TGEiCP) are presented. In addition, this condition is also used to test the vacuum stability of a general scalar potential.