Numerical comparisons of two effective methods for mixed complementarity problems

Jein-Shan Chen Shaohua Pan Ching-Yu Yang

Numerical Analysis and Scientific Computing mathscidoc:1910.43907

Journal of Computational and Applied Mathematics, 234, (3), 667-683, 2010.6
Recently there have two different effective methods proposed by Kanzow et al. in (Kanzow, 2001 [8]) and (Kanzow and Petra, 2004 [9]), respectively, which commonly use the FischerBurmeister (FB) function to recast the mixed complementarity problem (MCP) as a constrained minimization problem and a nonlinear system of equations, respectively. They all remark that their algorithms may be improved if the FB function is replaced by other NCP functions. Accordingly, in this paper, we employ the generalized FischerBurmeister (GFB) where the 2-norm in the FB function is relaxed to a general p-norm (p> 1) for the two methods and investigate how much the improvement is by changing the parameter p as well as which method is influenced more when we do so, by the performance profiles of iterations and function evaluations for the two methods with different p on MCPLIB collection.
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@inproceedings{jein-shan2010numerical,
  title={Numerical comparisons of two effective methods for mixed complementarity problems},
  author={Jein-Shan Chen, Shaohua Pan, and Ching-Yu Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224355417455436},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={234},
  number={3},
  pages={667-683},
  year={2010},
}
Jein-Shan Chen, Shaohua Pan, and Ching-Yu Yang. Numerical comparisons of two effective methods for mixed complementarity problems. 2010. Vol. 234. In Journal of Computational and Applied Mathematics. pp.667-683. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224355417455436.
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