Strictly semi-positive tensors and the boundedness of tensor complementarity problems

Abstract

In this paper, we prove that all H${}^{+}$(Z${}^{+}$)-eigenvalues of each principal sub-tensor of a strictly semi-positive tensor are positive. We define two new constants associated with H${}^{+}$(Z${}^{+}$)eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establish upper bounds of an important quantity whose positivity is a necessary and sufficient condition for a general tensor to be a strictly semi-positive tensor. The monotonicity and boundedness of such a quantity are established too. Furthermore, we present global error bound analysis for a class of the nonlinear complementarity problem defined by a strictly semi-positive tensor.

23 Pages. arXiv admin note: text overlap with arXiv:1508.02005

References in corpus (1)

• Properties of Solution set of Tensor Complementarity Problem

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