Z-tensors and complementarity problems

M. Seetharama Gowda, Ziyan Luo, Liqun Qi, and Naihua Xiu

Technical Report Number: trGOW15-02+


Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to Z-tensors (which are tensors with non-positive off-diagonal entries), we describe various equivalent conditions for a Z-tensor to have the global solvability property. We show by an example that the global solvability need not imply unique solvability and provide a sufficient and easily checkable condition for unique solvability.