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A smoothed NR neural network for solving nonlinear convex programs with second-order cone constraints

Xinhe Miao Jein-Shan Chen Chun-Hsu Ko

Machine Learning mathscidoc:1910.43906

Information Sciences, 268, 255-270, 2014.6
This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence and convergence of the trajectory of the neural network. Moreover, we show some stability properties for the considered neural network, such as the Lyapunov stability, asymptotic stability, and exponential stability. The examples in this paper provide a further demonstration of the effectiveness of the proposed neural network. This paper can be viewed as a follow-up version of [20], [26] because more stability results are obtained.
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@inproceedings{xinhe2014a,
  title={A smoothed NR neural network for solving nonlinear convex programs with second-order cone constraints},
  author={Xinhe Miao, Jein-Shan Chen, and Chun-Hsu Ko},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224315612148435},
  booktitle={Information Sciences},
  volume={268},
  pages={255-270},
  year={2014},
}
Xinhe Miao, Jein-Shan Chen, and Chun-Hsu Ko. A smoothed NR neural network for solving nonlinear convex programs with second-order cone constraints. 2014. Vol. 268. In Information Sciences. pp.255-270. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224315612148435.
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