Strictly semi-positive tensors and the boundedness of tensor complementarity problems
Optimization and Control
2022-02-09 v3
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.
Keywords
Cite
@article{arxiv.1509.01327,
title = {Strictly semi-positive tensors and the boundedness of tensor complementarity problems},
author = {Yisheng Song and Liqun Qi},
journal= {arXiv preprint arXiv:1509.01327},
year = {2022}
}
Comments
23 Pages. arXiv admin note: text overlap with arXiv:1508.02005