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Design of a kind of nonlinear neural networks for solving the inverse optimal value problem with convex constraints

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Abstract

In this paper, we consider how to design a kind of nonlinear neural networks for solving the inverse optimal value problem with convex constraints. Firstly, based on optimal theory, the inverse optimal value problem considered is changed to a class of nonlinear bilevel program problems. Secondly, under the given assumptions, the corresponding nonlinear bilevel programming problem can be reduced to the one-level programming problem. Thirdly, based on the gradient theory, a nonlinear neural network model is designed to solve this one-level programming problem. Moreover, by employing Lyapunov function approach, the proposed neural network is analyzed to be globally Lyapunov stable and capable of generating approximal optimal solution to the inverse optimal value problem. Finally, two illustrative examples are provided to verify the feasibility and the efficiency of the proposed method.

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Acknowledgments

The authors are extremely grateful to the Editor and the Reviewers for their valuable comments and suggestions, which help to enrich the content and improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China

    Huaiqin Wu, Kewang Wang, Qiangqiang Guo, Guohua Xu & Ning Li

Authors
  1. Huaiqin Wu
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  2. Kewang Wang
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  3. Qiangqiang Guo
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  4. Guohua Xu
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  5. Ning Li
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Corresponding author

Correspondence to Huaiqin Wu.

Additional information

This work was supported by the Natural Science Foundation of Hebei Province of China (A2011203103) and the Hebei Province Education Foundation of China (2009157).

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Wu, H., Wang, K., Guo, Q. et al. Design of a kind of nonlinear neural networks for solving the inverse optimal value problem with convex constraints. Int. J. Mach. Learn. & Cyber. 5, 85–92 (2014). https://doi.org/10.1007/s13042-012-0138-0

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  • DOI: https://doi.org/10.1007/s13042-012-0138-0

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