Abstract
In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+) -eigenvalues of each principal sub-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.
Original language | English |
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Pages (from-to) | 1407-1426 |
Number of pages | 20 |
Journal | Optimization Letters |
Volume | 11 |
Issue number | 7 |
DOIs | |
Publication status | Published - 1 Oct 2017 |
Keywords
- Eigenvalues
- Strictly semi-positive tensor
- Tensor complementarity problem
- Upper and lower bounds
ASJC Scopus subject areas
- Control and Optimization