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arXiv · 1905.06885

The dual Z-property for the Lorentz cone

S. Z. Németh
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Abstract

The Z-property of a linear map with respect to a cone is an extension of the notion of Z-matrices. In a recent paper of Orlitzky (see Corollary 6.2 in M. Orlitzky. Positive and $\mathbf{Z}$-operators on closed convex cones, Electron. J Linear Algebra, 444--458, 2018) the characterisation of cone-complementarity is given in terms of the dual of the cone of linear maps satisfying the Z-property. Therefore, it is meaningful to consider the problem of finding the dual cone of the cone of linear maps which have the Z-property with respect to a cone. This short note will solve this problem in the particular case when the Z-property is considered with respect to the Lorentz cone.

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S. Z. Németh. 2019-05-16. The dual Z-property for the Lorentz cone. https://arxiv.org/abs/1905.06885

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