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Constructions of complementarity functions and merit functions for circular cone complementarity problem


  • Xin-He Miao

    () (Tianjin University)

  • Shengjuan Guo

    () (Tianjin University)

  • Nuo Qi

    () (Tianjin University)

  • Jein-Shan Chen

    () (National Taiwan Normal University)


Abstract In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:coopap:v:63:y:2016:i:2:d:10.1007_s10589-015-9781-1
    DOI: 10.1007/s10589-015-9781-1

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    References listed on IDEAS

    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. repec:spr:compst:v:64:y:2006:i:3:p:495-519 is not listed on IDEAS
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