The cone of Z-transformations on Lorentz cone

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The cone of Z-transformations on Lorentz cone.pdf (351.39 KB)

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https://repository.uwyo.edu/ela/vol35/iss1/25/

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http://hdl.handle.net/11603/15876

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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2019-09

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journal articles postprints
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Citation of Original Publication

Németh, Sándor & Gowda, Muddappa. (2019). The cone of Z-transformations on the Lorentz cone. Electronic Journal of Linear Algebra. 35. 387-393. 10.13001/1081-3810.4083.

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Subjects

Z-transformation
Lorentz cone
Semidefinite cone
Copositive cone
Completely positive cone

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.