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arXiv · 1510.07933

Z-tensors and complementarity problems

M. Seetharama Gowda·Ziyan Luo·Liqun Qi·Naihua Xiu
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Abstract

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.

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M. Seetharama Gowda, Ziyan Luo, Liqun Qi, Naihua Xiu. 2015-10-27. Z-tensors and complementarity problems. https://arxiv.org/abs/1510.07933

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