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How to project onto extended second order cones

Author

Listed:
  • O. P. Ferreira

    (IME/UFG)

  • S. Z. Németh

    (University of Birmingham)

Abstract

The extended second order cones were introduced by Németh and Zhang (J Optim Theory Appl 168(3):756–768, 2016) for solving mixed complementarity problems and variational inequalities on cylinders. Sznajder (J Glob Optim 66(3):585–593, 2016) determined the automorphism groups and the Lyapunov or bilinearity ranks of these cones. Németh and Zhang (Positive operators of extended Lorentz cones, 2016. arXiv:1608.07455v2 ) found both necessary conditions and sufficient conditions for a linear operator to be a positive operator of an extended second order cone. In this note we give formulas for projecting onto the extended second order cones. In the most general case the formula depends on a piecewise linear equation for one real variable which is solved by using numerical methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:4:d:10.1007_s10898-017-0587-9
    DOI: 10.1007/s10898-017-0587-9
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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. Sándor Zoltán Németh & Guohan Zhang, 2016. "Extended Lorentz Cones and Variational Inequalities on Cylinders," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 756-768, March.
    3. Kai Ye & Panos Parpas & Berç Rustem, 2012. "Robust portfolio optimization: a conic programming approach," Computational Optimization and Applications, Springer, vol. 52(2), pages 463-481, June.
    4. Pedro Gajardo & Alberto Seeger, 2014. "Equilibrium problems involving the Lorentz cone," Journal of Global Optimization, Springer, vol. 58(2), pages 321-340, February.
    5. Roman Sznajder, 2016. "The Lyapunov rank of extended second order cones," Journal of Global Optimization, Springer, vol. 66(3), pages 585-593, November.
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