Journal of Global Optimization

, Volume 66, Issue 3, pp 585–593 | Cite as

The Lyapunov rank of extended second order cones

  • Roman SznajderEmail author


In this paper, we investigate the structure of Lyapunov-like transformations on the extended second order cone, considered as a multivariate version of topheavy cone with respect to an arbitrary norm in a Euclidean space. As a by-product, we compute the Lyapunov rank of the extended second order cone. We also show the irreducibility of such a cone.


Extended second order cone Irreducibility Lyapunov rank Lyapunov-like transformation Proper cone 

Mathematics Subject Classification

90C33 17C20 17C55 



I wish to thank the referee, whose questions helped me localize a gap in the proof of Theorem 1. I am grateful to Dr. M.S. Gowda for turning my attention to the paper [10], and for the comments which contributed to the final shape of the proof of Theorem 1.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsBowie State UniversityBowieUSA

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