The cone of Z-transformations on the Lorentz cone

Sandor Nemeth, Muddappa Seetharama Gowda

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1 Citation (Scopus)
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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 languageEnglish
Article number25
Pages (from-to)387-393
Number of pages7
JournalElectronic Journal of Linear Algebra
Issue number1
Publication statusPublished - 12 Sept 2019


  • Z-transformation
  • Lorentz cone
  • semidefinite cone
  • copositive cone
  • completely positive cone


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