The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems.

In this paper, we consider the global uniqueness and solvability (GUS) of tensor complementarity problems for special power Lipschitz tensors (SPL-tensors). It is shown that a SPL-tensor is a P-tensor, but not necessarily an H-tensor. And it is also proved that tensor complementarity problems of SPL-tensors have the GUS-property. In addition, we propose modulus-based tensor splitting methods to solve the tensor complementarity problem. We consider both stand and accelerated tensor splitting methods for solving the reformulated fixed-point equations of tensor complementarity problems. The convergence analysis of two classes of modulus-based iterative methods is discussed when the system tensors are power Lipschitz tensors. Numerical examples are given to illustrate the effectiveness and efficiency of the presented approaches. [ABSTRACT FROM AUTHOR]