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A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints

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  • Liu, Xiaolan
  • Zhou, Mi

Abstract

In this paper, a one-layer recurrent network is proposed for solving a non-smooth convex optimization subject to linear inequality constraints. Compared with the existing neural networks for optimization, the proposed neural network is capable of solving more general convex optimization with linear inequality constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds.

Suggested Citation

  • Liu, Xiaolan & Zhou, Mi, 2016. "A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 39-46.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:39-46
    DOI: 10.1016/j.chaos.2016.03.009
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    References listed on IDEAS

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    1. Y. S. Xia & J. Wang, 2000. "On the Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 129-150, July.
    2. Jong-Shi Pang, 1987. "A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 474-484, August.
    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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    Cited by:

    1. Leonid B. Sokolinsky & Irina M. Sokolinskaya, 2023. "Apex Method: A New Scalable Iterative Method for Linear Programming," Mathematics, MDPI, vol. 11(7), pages 1-28, March.

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