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On merit functions for p-order cone complementarity problem

Author

Listed:
  • Xin-He Miao

    (Tianjin University)

  • Yu-Lin Chang

    (National Taiwan Normal University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

Abstract

Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.

Suggested Citation

  • Xin-He Miao & Yu-Lin Chang & Jein-Shan Chen, 2017. "On merit functions for p-order cone complementarity problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 155-173, May.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:1:d:10.1007_s10589-016-9889-y
    DOI: 10.1007/s10589-016-9889-y
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    References listed on IDEAS

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    1. Jein-Shan Chen, 2006. "Two classes of merit functions for the second-order cone complementarity problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 495-519, December.
    2. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
    3. J.-S. Chen, 2007. "Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 459-473, December.
    4. Xin-He Miao & Shengjuan Guo & Nuo Qi & Jein-Shan Chen, 2016. "Constructions of complementarity functions and merit functions for circular cone complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 495-522, March.
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    Cited by:

    1. Xin-He Miao & Yen-chi Roger Lin & Jein-Shan Chen, 2017. "A Note on the Paper “The Algebraic Structure of the Arbitrary-Order Cone”," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 1066-1070, June.

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