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The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem

Jein-Shan Chen

Optimization and Control mathscidoc:1910.43874

Journal of Global Optimization, 36, (4), 565-580, 2006.12
This paper is a follow-up of the work [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)] where an NCP-function and a descent method were proposed for the nonlinear complementarity problem. An unconstrained reformulation was formulated due to a merit function based on the proposed NCP-function. We continue to explore properties of the merit function in this paper. In particular, we show that the gradient of the merit function is globally Lipschitz continuous which is important from computational aspect. Moreover, we show that the merit function is <i>SC</i> <sup>1</sup> function which means it is continuously differentiable and its gradient is semismooth. On the other hand, we provide an alternative proof, which uses the new properties of the merit function, for the convergence result of the descent method considered in [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)].
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@inproceedings{jein-shan2006the,
  title={The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem},
  author={Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223222223325403},
  booktitle={Journal of Global Optimization},
  volume={36},
  number={4},
  pages={565-580},
  year={2006},
}
Jein-Shan Chen. The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem. 2006. Vol. 36. In Journal of Global Optimization. pp.565-580. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020223222223325403.
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