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A one-parametric class of merit functions for the second-order cone complementarity problem

Jein-Shan Chen Shaohua Pan

Optimization and Control mathscidoc:1910.43884

Computational Optimization and Applications, 45, (3), 581-606, 2010.4
We investigate a one-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) which is closely related to the popular FischerBurmeister (FB) merit function and natural residual merit function. In fact, it will reduce to the FB merit function if the involved parameter <i></i> equals 2, whereas as <i></i> tends to zero, its limit will become a multiple of the natural residual merit function. In this paper, we show that this class of merit functions enjoys several favorable properties as the FB merit function holds, for example, the smoothness. These properties play an important role in the reformulation method of an unconstrained minimization or a nonsmooth system of equations for the SOCCP. Numerical results are reported for some convex second-order cone programs (SOCPs) by solving the unconstrained minimization reformulation of the KKT optimality conditions, which indicate that the
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@inproceedings{jein-shan2010a,
  title={A one-parametric class of merit functions for the second-order cone complementarity problem},
  author={Jein-Shan Chen, and Shaohua Pan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223646315314413},
  booktitle={Computational Optimization and Applications},
  volume={45},
  number={3},
  pages={581-606},
  year={2010},
}
Jein-Shan Chen, and Shaohua Pan. A one-parametric class of merit functions for the second-order cone complementarity problem. 2010. Vol. 45. In Computational Optimization and Applications. pp.581-606. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223646315314413.
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