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An R-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized FischerBurmeister merit function

Jein-Shan Chen Hung-Ta Gao Shaohua Pan

Optimization and Control mathscidoc:1910.43891

Journal of Computational and Applied Mathematics, 232, (2), 455-471, 2009.10
In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the generalized FischerBurmeister merit function: p (a, b)= 1 2 [(a, b) p(a+ b)] 2, and observed that the choice of the parameter p has a great influence on the numerical performance of the algorithm. In this paper, we analyze the phenomenon theoretically for a derivative-free descent algorithm which is based on a penalized form of p and uses a different direction from that of Chen and Pan. More specifically, we show that the algorithm proposed is globally convergent and has a locally R-linear convergence rate, and furthermore, its convergence rate will become worse when the parameter p decreases
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@inproceedings{jein-shan2009an,
  title={An R-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized FischerBurmeister merit function},
  author={Jein-Shan Chen, Hung-Ta Gao, and Shaohua Pan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223852083294420},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={232},
  number={2},
  pages={455-471},
  year={2009},
}
Jein-Shan Chen, Hung-Ta Gao, and Shaohua Pan. An R-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized FischerBurmeister merit function. 2009. Vol. 232. In Journal of Computational and Applied Mathematics. pp.455-471. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223852083294420.
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