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A feedback neural network for solving convex quadratic bi-level programming problems

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Abstract

In this paper, a feedback neural network model is proposed for solving a class of convex quadratic bi-level programming problems based on the idea of successive approximation. Differing from existing neural network models, the proposed neural network has the least number of state variables and simple structure. Based on Lyapunov theories, we prove that the equilibrium point sequence of the feedback neural network can approximately converge to an optimal solution of the convex quadratic bi-level problem under certain conditions, and the corresponding sequence of the function value approximately converges to the optimal value of the convex quadratic bi-level problem. Simulation experiments on three numerical examples and a portfolio selection problem are provided to show the efficiency and performance of the proposed neural network approach.

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Acknowledgments

The authors are thankful to their editor and anonymous referees for their valuable comments and suggestions that have improved the quality of the paper significantly.

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Authors and Affiliations

  1. School of Science, Information Technology and Engineering, University of Ballarat, Ballarat, VIC, 3353, Australia

    Jueyou Li, Chaojie Li & Zhiyou Wu

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Jueyou Li & Zhiyou Wu

  3. Department of Computer Science, Chongqing University of Education, Chongqing, 400067, People’s Republic of China

    Junjian Huang

Authors
  1. Jueyou Li
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  2. Chaojie Li
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  3. Zhiyou Wu
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  4. Junjian Huang
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Corresponding author

Correspondence to Chaojie Li.

Additional information

This research was partially supported by KJ120616, cstc2013jjB00001 and SRF for ROCS, SEM.

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Li, J., Li, C., Wu, Z. et al. A feedback neural network for solving convex quadratic bi-level programming problems. Neural Comput & Applic 25, 603–611 (2014). https://doi.org/10.1007/s00521-013-1530-8

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  • DOI: https://doi.org/10.1007/s00521-013-1530-8

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