Abstract
In this paper, the structural properties of the cone of Z-transformations on the Lorentz cone are described in terms of the semidefinite cone and copositive/completely positive cones induced by the Lorentz cone and its boundary. In particular, its dual is described as a slice of the semidefinite cone as well as a slice of the completely positive cone of the Lorentz cone. This provides an example of an instance where a conic linear program on a completely positive cone is reduced to a problem on the semidefinite cone.
Original language | English |
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Article number | 25 |
Pages (from-to) | 387-393 |
Number of pages | 7 |
Journal | Electronic Journal of Linear Algebra |
Volume | 35 |
Issue number | 1 |
DOIs | |
Publication status | Published - 12 Sept 2019 |
Keywords
- Z-transformation
- Lorentz cone
- semidefinite cone
- copositive cone
- completely positive cone