Global uniqueness and solvability of tensor complementarity problems for $\mathcal {H}_{+}$-tensors

Abstract

Inthis paper, we study the global uniqueness and solvability of tensor complementarity problems for $\mathcal {H}_{+}$-tensors. We obtain a sufficient condition of the global uniqueness and solvability of tensor complementarity problems for $\mathcal {H}_{+}$-tensors. We present nonlinear dynamical system models for solving the tensor complementarity problem (TCP). We prove that the presented dynamical system models are stable in the sense of Lyapunov stability theory for considering three classes of structured tensors. The computer simulation results further substantiate that the considered dynamical system can be used to solve the TCP.