On a Class of Semi-Positive Tensors in Tensor Complementarity Problem

Ya-nan Zheng () and Wei Wu ()
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Ya-nan Zheng: Tianjin University
Wei Wu: Tianjin University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 1, No 6, 127-136

Abstract: Abstract Recently, the tensor complementarity problem has been investigated in the literature. In this paper, we extend a class of structured matrices to higher-order tensors; the corresponding tensor complementarity problem has a unique solution for any nonzero nonnegative vector. We discuss their relationships with semi-positive tensors and strictly semi-positive tensors. We also study the property of such a structured tensor. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. We also give two equivalent formulations of such a structured tensor.

Keywords: Tensor complementarity problem; E-tensor; Strictly semi-positive tensor; Principal sub-tensor; 15A18; 15A69; 90C33 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1262-0

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