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A novel neurodynamic reaction-diffusion model for solving linear variational inequality problems and its application

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  • Sha, Chunlin
  • Zhao, Hongyong

Abstract

In this paper, we present a new delayed projection neural network with reaction-diffusion terms for solving linear variational inequality problems. The proposed neural network possesses a simple one-layer structure. By employing the differential inequality technique and constructing a new Lyapunov–Krasovskii functional, we derive some novel sufficient conditions ensuring the globally exponential stability. These conditions are dependent on diffusions and the monotonicity assumption is unnecessary. Furthermore, the considered neural network can solve quadratic programming problems. Finally, several applicable examples are provided to illustrate the satisfactory performance of the proposed neural network.

Suggested Citation

  • Sha, Chunlin & Zhao, Hongyong, 2019. "A novel neurodynamic reaction-diffusion model for solving linear variational inequality problems and its application," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 57-75.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:57-75
    DOI: 10.1016/j.amc.2018.10.023
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    References listed on IDEAS

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    1. Yang, Yongqing & Cao, Jinde & Xu, Xianyun & Hu, Manfeng & Gao, Yun, 2014. "A new neural network for solving quadratic programming problems with equality and inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 103-112.
    2. Huang, Tingwen, 2007. "Exponential stability of delayed fuzzy cellular neural networks with diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 658-664.
    3. Y. S. Xia, 2004. "Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 627-649, September.
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