Abstract
In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. 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. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 854-873 |
| Number of pages | 20 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 165 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jun 2015 |
Keywords
- (formula presented)
- B tensor
- Eigenvalues
- P tensor
- Principal sub-tensor
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics