On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

Shaohua Pan Sangho Kum Yongdo Lim Jein-Shan Chen

Optimization and Control mathscidoc:1910.43901

Mathematics of Computation, 83, (287), 1143-1171, 2014
It has been an open question whether the family of merit functions $\psi _p\(p> 1) $, the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that \psi _p is smooth for \psi _p , and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of \psi _p on the performance of the merit function method based on \psi _p .
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@inproceedings{shaohua2014on,
  title={On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem},
  author={Shaohua Pan, Sangho Kum, Yongdo Lim, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224149480190430},
  booktitle={Mathematics of Computation},
  volume={83},
  number={287},
  pages={1143-1171},
  year={2014},
}
Shaohua Pan, Sangho Kum, Yongdo Lim, and Jein-Shan Chen. On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem. 2014. Vol. 83. In Mathematics of Computation. pp.1143-1171. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224149480190430.
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