Neural networks based on three classes of NCP-functions for solving nonlinear complementarity problems

Jan Harold Alcantara Jein-Shan Chen

Optimization and Control mathscidoc:1910.43962

Neurocomputing, 2019.5
In this paper, we consider a family of neural networks for solving nonlinear complementarity problems (NCP). The neural networks are constructed from the merit functions based on three classes of NCP-functions: the generalized natural residual function and its two symmetrizations. In this paper, we first characterize the stationary points of the induced merit functions. Growth behavior of the complementarity functions is also described, as this will play an important role in describing the level sets of the merit functions. In addition, the stability of the steepest descent-based neural network model for NCP is analyzed. We provide numerical simulations to illustrate the theoretical results, and also compare the proposed neural networks with existing neural networks based on other well-known NCP-functions. Numerical results indicate that the performance of the neural network is better when the parameter <i>p</i> associated
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@inproceedings{jan2019neural,
  title={Neural networks based on three classes of NCP-functions for solving nonlinear complementarity problems},
  author={Jan Harold Alcantara, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230217189154491},
  booktitle={Neurocomputing},
  year={2019},
}
Jan Harold Alcantara, and Jein-Shan Chen. Neural networks based on three classes of NCP-functions for solving nonlinear complementarity problems. 2019. In Neurocomputing. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230217189154491.
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