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Neural networks for solving second-order cone constrained variational inequality problem

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Abstract

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, China

    Juhe Sun

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jein-Shan Chen

  3. Department of Electrical Engineering, I-Shou University, Kaohsiung, 840, Taiwan

    Chun-Hsu Ko

Authors
  1. Juhe Sun
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  2. Jein-Shan Chen
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  3. Chun-Hsu Ko
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Corresponding author

Correspondence to Jein-Shan Chen.

Additional information

J. Sun is also affiliated with Department of Mathematics, National Taiwan Normal University.

J.-S. Chen is member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan.

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Sun, J., Chen, JS. & Ko, CH. Neural networks for solving second-order cone constrained variational inequality problem. Comput Optim Appl 51, 623–648 (2012). https://doi.org/10.1007/s10589-010-9359-x

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