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Discovery of new complementarity functions for NCP and SOCCP

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, P.R. China

    Peng-Fei Ma

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jein-Shan Chen & Chien-Hao Huang

  3. Department of Electrical Engineering, I-Shou University, Kaohsiung, 840, Taiwan

    Chun-Hsu Ko

Authors
  1. Peng-Fei Ma
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  2. Jein-Shan Chen
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  3. Chien-Hao Huang
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  4. Chun-Hsu Ko
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Corresponding author

Correspondence to Jein-Shan Chen.

Additional information

Communicated by Jinyun Yuan.

Peng-Fei Ma This research was supported by a grant from the National Natural Science Foundation of China(No.11626212).

Jein-Shan Chen The author’s work is supported by Ministry of Science and Technology, Taiwan.

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Ma, PF., Chen, JS., Huang, CH. et al. Discovery of new complementarity functions for NCP and SOCCP. Comp. Appl. Math. 37, 5727–5749 (2018). https://doi.org/10.1007/s40314-018-0660-0

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  • DOI: https://doi.org/10.1007/s40314-018-0660-0

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