Discovery of new complementarity functions for NCP and SOCCP

Peng-Fei Ma Jein-Shan Chen Chien-Hao Huang Chun-Hsu Ko

Optimization and Control mathscidoc:1910.43921

Computational and Applied Mathematics, 37, (5), 5727-5749, 2018.11
It is well known that complementarity functions play an important role in dealing with complementarity problems. In this paper, we propose a few new classes of complementarity functions for nonlinear complementarity problems and second-order cone complementarity problems. The constructions of such new complementarity functions are based on discrete generalization which is a novel idea in contrast to the continuous generalization of FischerBurmeister function. Surprisingly, these new families of complementarity functions possess continuous differentiability even though they are discrete-oriented extensions. This feature enables that some methods like derivative-free algorithm can be employed directly for solving nonlinear complementarity problems and second-order cone complementarity problems. This is a new discovery to the literature and we believe that such new complementarity functions
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@inproceedings{peng-fei2018discovery,
  title={Discovery of new complementarity functions for NCP and SOCCP},
  author={Peng-Fei Ma, Jein-Shan Chen, Chien-Hao Huang, and Chun-Hsu Ko},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224846314223450},
  booktitle={Computational and Applied Mathematics},
  volume={37},
  number={5},
  pages={5727-5749},
  year={2018},
}
Peng-Fei Ma, Jein-Shan Chen, Chien-Hao Huang, and Chun-Hsu Ko. Discovery of new complementarity functions for NCP and SOCCP. 2018. Vol. 37. In Computational and Applied Mathematics. pp.5727-5749. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224846314223450.
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