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International Symposium on Neural Networks

ISNN 2015: Advances in Neural Networks – ISNN 2015 pp 418–425Cite as

A Neurodynamic Optimization Approach to Bilevel Linear Programming

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

Abstract

This paper presents new results on neurodynamic optimization approach to solve bilevel linear programming problems (BLPPs) with linear inequality constraints. A sub-gradient recurrent neural network is proposed for solving the BLPPs. It is proved that the state convergence time period is finite and can be quantitatively estimated. Compared with existing recurrent neural networks for BLPPs, the proposed neural network does not have any design parameter and can solve the BLPPs in finite time. Some numerical examples are introduced to show the effectiveness of the proposed neural network.

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References

  1. Aubin, J.P., Cellina, A.: Differential inclusions. Springer, Berlin (1984)

    Book  MATH  Google Scholar 

  2. Calvete, H.I., Gale, C.: On linear bilevel problems with multiple objectives at the lower level. Omega 39(1), 33–40 (2011)

    Article  Google Scholar 

  3. Cheng, L., Hou, Z.G., Lin, Y., Tan, M., Zhang, W.C., Wu, F.: Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks. IEEE Trans. Neural Networks 22(5), 714–726 (2011)

    Article  Google Scholar 

  4. Cichocki, A., Unbehauen, R.: Neural networks for optimization and signal processing. Wiley (1993)

    Google Scholar 

  5. Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Annals of Operations Research 153(1), 235–256 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. He, X., Li, C., Huang, T., Li, C.: Neural network for solving convex quadratic bilevel programming problems. Neural Networks 51, 17–25 (2014)

    Article  MATH  Google Scholar 

  7. He, X., Li, C., Huang, T., Li, C., Huang, J.: A recurrent neural network for solving bilevel linear programming problem. IEEE Transactions on Neural Networks and Learning Systems 25(4), 824–830 (2014)

    Article  Google Scholar 

  8. Jiang, Y., Li, X., Huang, C., Wu, X.: An augmented lagrangian multiplier method based on a chks smoothing function for solving nonlinear bilevel programming problems. Knowledge-Based Systems 55, 9–14 (2014)

    Article  Google Scholar 

  9. Kennedy, M.P., Chua, L.O.: Neural networks for nonlinear programming. IEEE Trans. Circuits and Systems I: Regular Papers 35(5), 554–562 (1988)

    Article  MathSciNet  Google Scholar 

  10. Kuo, R., Huang, C.: Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Computers & Mathematics with Applications 58(4), 678–685 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lv, Y., Chen, Z., Wan, Z.: A neural network for solving a convex quadratic bilevel programming problem. Journal of Computational and Applied Mathematics 234(2), 505–511 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mersha, A.G., Dempe, S.: Feasible direction method for bilevel programming problem. Optimization 61(5), 597–616 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Muu, L.D., Quy, N.V.: A global optimization method for solving convex quadratic bilevel programming problems. J. Global Optimization 26(2), 199–219 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Qin, S., Xue, X.: Global exponential stability and global convergence in finite time of neural networks with discontinuous activations. Neural Processing Letters 29(3), 189–204 (2009)

    Article  Google Scholar 

  15. Qin, S., Xue, X.: Dynamical analysis of neural networks of subgradient system. IEEE Trans. Automat. Contr. 55(10), 2347–2352 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Scholtes, S.: Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM Journal on Optimization 11(4), 918–936 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shih, H.S., Wen, U.P., Lee, S., Lan, K.M., Hsiao, H.C.: A neural network approach to multiobjective and multilevel programming problems. Computers & Mathematics with Applications 48(1-2), 95–108 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wan, Z., Mao, L., Wang, G.: Estimation of distribution algorithm for a class of nonlinear bilevel programming problems. Information Sciences 256, 184–196 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wen, U.P., Hsu, S.T.: Linear bi-level programming problems–a review. Journal of the Operational Research Society, 125–133 (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, China

    Sitian Qin

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Xinyi Le & Jun Wang

  3. School of Control Science and Engineering, Dalian University of Technology, Dalian, China

    Sitian Qin & Jun Wang

Authors
  1. Sitian Qin
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  2. Xinyi Le
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  3. Jun Wang
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Corresponding author

Correspondence to Sitian Qin .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, China

    Xiaolin Hu

  2. Fuzhou University, Fuzhou, China

    Yousheng Xia

  3. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China

    Yunong Zhang

  4. Chinese Academy of Sciences, Institute of Automation, Beijing, China

    Dongbin Zhao

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© 2015 Springer International Publishing Switzerland

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Qin, S., Le, X., Wang, J. (2015). A Neurodynamic Optimization Approach to Bilevel Linear Programming. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_46

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  • DOI: https://doi.org/10.1007/978-3-319-25393-0_46

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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