Discovery of new complementarity functions for NCP and SOCCP

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

Research output: Contribution to journalArticle

2 Citations (Scopus)


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 Fischer–Burmeister 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 can also be used in many other contexts.

Original languageEnglish
Pages (from-to)5727-5749
Number of pages23
JournalComputational and Applied Mathematics
Issue number5
Publication statusPublished - 2018 Nov 1



  • Complementarity function
  • Natural residual
  • NCP

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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