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The Lyapunov rank of extended second order cones

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  • Roman Sznajder

    (Bowie State University)

Abstract

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.

Suggested Citation

  • Roman Sznajder, 2016. "The Lyapunov rank of extended second order cones," Journal of Global Optimization, Springer, vol. 66(3), pages 585-593, November.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:3:d:10.1007_s10898-016-0445-1
    DOI: 10.1007/s10898-016-0445-1
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    References listed on IDEAS

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    1. S. Németh & G. Zhang, 2015. "Extended Lorentz cones and mixed complementarity problems," Journal of Global Optimization, Springer, vol. 62(3), pages 443-457, July.
    2. Jiyuan Tao & M. Seetharama Gowda, 2013. "A Representation Theorem For Lyapunov-Like Transformations On Euclidean Jordan Algebras," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-11.
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    Cited by:

    1. Sándor Zoltán Németh & Lianghai Xiao, 2018. "Linear Complementarity Problems on Extended Second Order Cones," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 269-288, February.
    2. Yingchao Gao & Sándor Zoltán Németh & Roman Sznajder, 2022. "The Monotone Extended Second-Order Cone and Mixed Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 381-407, June.
    3. O. P. Ferreira & S. Z. Németh, 2018. "How to project onto extended second order cones," Journal of Global Optimization, Springer, vol. 70(4), pages 707-718, April.

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