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

Shaohua Pan Jein-Shan Chen

Optimization and Control mathscidoc:1910.43879

Journal of Mathematical Analysis and Applications, 355, (1), 195-215, 2009.7
In this paper, we extend the one-parametric class of merit functions proposed by Kanzow and Kleinmichel [C. Kanzow, H. Kleinmichel, A new class of semismooth Newton-type methods for nonlinear complementarity problems, Comput. Optim. Appl. 11 (1998) 227251] for the nonnegative orthant complementarity problem to the general symmetric cone complementarity problem (SCCP). We show that the class of merit functions is continuously differentiable everywhere and has a globally Lipschitz continuous gradient mapping. From this, we particularly obtain the smoothness of the FischerBurmeister merit function associated with symmetric cones and the Lipschitz continuity of its gradient. In addition, we also consider a regularized formulation for the class of merit functions which is actually an extension of one of the NCP function classes studied by [C. Kanzow, Y. Yamashita, M. Fukushima, New NCP functions and
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@inproceedings{shaohua2009a,
  title={A one-parametric class of merit functions for the symmetric cone complementarity problem},
  author={Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223423361430408},
  booktitle={Journal of Mathematical Analysis and Applications},
  volume={355},
  number={1},
  pages={195-215},
  year={2009},
}
Shaohua Pan, and Jein-Shan Chen. A one-parametric class of merit functions for the symmetric cone complementarity problem. 2009. Vol. 355. In Journal of Mathematical Analysis and Applications. pp.195-215. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223423361430408.
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