The Lyapunov rank of extended second order cones
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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.
KeywordsExtended second order cone Irreducibility Lyapunov rank Lyapunov-like transformation Proper cone
Mathematics Subject Classification90C33 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 , and for the comments which contributed to the final shape of the proof of Theorem 1.
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