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A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems

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Abstract

In this paper, a recurrent neural network with a new tunable activation is proposed to solve a kind of convex quadratic bilevel programming problem. It is proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov, and the state of the proposed neural network converges to an equilibrium point in finite time. In contrast to the existing related neurodynamic approaches, the proposed neural network in this paper is capable of solving the convex quadratic bilevel programming problem in finite time. Moreover, the finite convergence time can be quantitatively estimated. Finally, two numerical examples are presented to show the effectiveness of the proposed recurrent neural network.

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Acknowledgements

This research is supported by the National Science Foundation of China (61403101, 61401283, 11471088) and Educational Commission of Guangdong Province, China (2014KTSCX113).

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Authors and Affiliations

  1. Institute of Intelligent Computing Science, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Jiqiang Feng

  2. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, People’s Republic of China

    Sitian Qin, Fengli Shi & Xiaoyue Zhao

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  1. Jiqiang Feng
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  2. Sitian Qin
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  3. Fengli Shi
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  4. Xiaoyue Zhao
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Correspondence to Sitian Qin.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems”.

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Feng, J., Qin, S., Shi, F. et al. A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems. Neural Comput & Applic 30, 3399–3408 (2018). https://doi.org/10.1007/s00521-017-2926-7

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  • DOI: https://doi.org/10.1007/s00521-017-2926-7

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