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Equilibrium problems involving the Lorentz cone

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  • Pedro Gajardo
  • Alberto Seeger

Abstract

We study a general equilibrium model formulated as a smooth system of equations coupled with complementarity conditions relative to the $$n$$ -dimensional Lorentz cone. For the purpose of analysis, as well as for the design of algorithms, we exploit the fact that the Lorentz cone is representable as a cone of squares in a suitable Euclidean Jordan algebra. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Pedro Gajardo & Alberto Seeger, 2014. "Equilibrium problems involving the Lorentz cone," Journal of Global Optimization, Springer, vol. 58(2), pages 321-340, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:321-340
    DOI: 10.1007/s10898-013-0076-8
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    References listed on IDEAS

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    1. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
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    Cited by:

    1. 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.
    2. Dezhou Kong & Lishan Liu & Yonghong Wu, 2017. "Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 117-130, April.
    3. Orizon Pereira Ferreira & Yingchao Gao & Sándor Zoltán Németh & Petra Renáta Rigó, 2024. "Gradient projection method on the sphere, complementarity problems and copositivity," Journal of Global Optimization, Springer, vol. 90(1), pages 1-25, September.

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