Skip to main content
SpringerLink
Log in

A Projection Neural Network with Time Delays for Solving Linear Variational Inequality Problems and Its Applications

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, a new projection neural network with discrete and distributed delays is presented for solving linear variational inequality problems. Some novel sufficient conditions ensuring globally exponential stability are derived by employing matrix measure and differential inequality technique, and the easily checkable conditions are less restrictive. Furthermore, based on the Lagrange multiplier, the proposed neural network can solve the quadratic programming problems. Finally, some simulation results with applications to finance and image fusion are given to demonstrate the effective performance of the neural network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear programming: theory and algorithms (Wiley, New Jersey, 2013)

    MATH  Google Scholar 

  2. L. Cheng, Z. Hou, M. Tan, A delayed projection neural network for solving linear variational inequalities. IEEE Trans. Neural Netw. 20(6), 915–925 (2009)

    Article  Google Scholar 

  3. L. Cheng, Z. Hou, M. Tan, Solving linear variational inequalities by projection neural network with time-varying delays. Phys. Lett. A 373(20), 1739–1743 (2009)

    Article  MATH  Google Scholar 

  4. M.C. Ferris, J. Pang, Engineering and economic applications of complementarity problems. SIAM Rev. 39(4), 669–713 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. X. Gao, L. Liao, L. Qi, A novel neural network for variational inequalities with linear and nonlinear constraints. IEEE Trans. Neural Netw. 16(6), 1305–1317 (2005)

    Article  Google Scholar 

  6. K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics (Springer Science & Business Media, New York, 2013)

    MATH  Google Scholar 

  7. R.A. Haugen, R.A. Haugen, Modern investment theory (Prentice Hall, New Jersey, 1990)

    MATH  Google Scholar 

  8. B. He, H. Yang, A neural network model for monotone linear asymmetric variational inequalities. IEEE Trans. Neural Netw. 11(1), 3–16 (2000)

    Article  MathSciNet  Google Scholar 

  9. D. Hu, H. Huang, T. Huang, Design of an arcak-type generalized h\(\_\)2 filter for delayed static neural networks. Circuits Syst. Signal Process. 33(11), 3635–3648 (2014)

    Article  MathSciNet  Google Scholar 

  10. X. Hu, J. Wang, A recurrent neural network for solving a class of general variational inequalities. IEEE Trans. Syst. Man Cybern. B Cybern. 37(3), 528–539 (2007)

    Article  Google Scholar 

  11. B. Huang, G. Hui, D. Gong, Z. Wang, X. Meng, A projection neural network with mixed delays for solving linear variational inequality. Neurocomputing 125, 28–32 (2014)

    Article  Google Scholar 

  12. B. Huang, H. Zhang, D. Gong, Z. Wang, A new result for projection neural networks to solve linear variational inequalities and related optimization problems. Neural Comput. Appl. 23(2), 357–362 (2013)

    Article  Google Scholar 

  13. D. Kinderlehrer, G. Stampacchia, An introduction to variational inequalities and their applications (SIAM, New York, 2000)

    Book  MATH  Google Scholar 

  14. D. Li, R.M. Mersereau, S. Simske, Blind image deconvolution through support vector regression. IEEE Trans. Neural Netw. 18(3), 931–935 (2007)

    Article  Google Scholar 

  15. F. Li, Delayed Lagrangian neural networks for solving convex programming problems. Neurocomputing 73(10), 2266–2273 (2010)

    Article  Google Scholar 

  16. Q. Liu, T. Huang, J. Wang, One-layer continuous and discrete-time projection neural networks for solving variational inequalities and related optimization problems. IEEE Trans. Netw. Learn. Syst. 25(7), 1308–1318 (2014)

    Article  Google Scholar 

  17. Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization. IEEE Trans. Neural Netw. 26, 99–109 (2012)

    Article  MATH  Google Scholar 

  18. R. Lu, H. Li, Y. Zhu, Quantized h\(_\infty \) filtering for singular time-varying delay systems with unreliable communication channel. Circuits Syst. Signal Process. 31(2), 521–538 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Lu, H. Wu, J. Bai, New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. J. Franklin Inst. 351(3), 1386–1399 (2014)

    Article  MathSciNet  Google Scholar 

  20. R. Lu, Y. Xu, A. Xue, H\(_\infty \) filtering for singular systems with communication delays. Signal Process. 90(4), 1240–1248 (2010)

    Article  MATH  Google Scholar 

  21. A. Nazemi, A neural network model for solving convex quadratic programming problems with some applications. Eng. Appl. Artif. Intell. 32, 54–62 (2014)

    Article  Google Scholar 

  22. S. Qin, D. Fan, P. Su, Q. Liu, A simplified recurrent neural network for pseudoconvex optimization subject to linear equality constraints. Commun. Nonlinear Sci. Numer. Simul. 19(4), 789–798 (2014)

    Article  MathSciNet  Google Scholar 

  23. C. Sha, H. Zhao, F. Ren, A new delayed projection neural network for solving quadratic programming problems with equality and inequality constraints. Neurocomputing (2015). doi:10.1016/j.neucom.2015.05.006

  24. D. Tank, J.J. Hopfield, Simple ’neural’ optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 33(5), 533–541 (1986)

    Article  Google Scholar 

  25. Q. Wang, B. Du, J. Lam, M.Z. Chen, Stability analysis of Markovian jump systems with multiple delay components and polytopic uncertainties. Circuits Syst. Signal Process. 31(1), 143–162 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Y. Xia, Further results on global convergence and stability of globally projected dynamical systems. J. Optim. Theory Appl. 122(3), 627–649 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. Xia, H. Leung, E. Bossé, Neural data fusion algorithms based on a linearly constrained least square method. IEEE Trans. Neural Netw. 13(2), 320–329 (2002)

    Article  Google Scholar 

  28. Y. Xia, J. Wang, A one-layer recurrent neural network for support vector machine learning. IEEE Trans. Syst. Man Cybern. B Cybern. 34(2), 1261–1269 (2004)

    Article  Google Scholar 

  29. Y. Yang, J. Cao, Solving quadratic programming problems by delayed projection neural network. IEEE Trans. Neural Netw. 17(6), 1630–1634 (2006)

    Article  Google Scholar 

  30. Y. Yang, J. Cao, X. Xu, M. Hu, Y. Gao, A new neural network for solving quadratic programming problems with equality and inequality constraints. Math. Comput. Simul. 101, 103–112 (2014)

    Article  MathSciNet  Google Scholar 

  31. H. Zhang, B. Huang, D. Gong, Z. Wang, New results for neutral-type delayed projection neural network to solve linear variational inequalities. Neural Comput. Appl. 23(6), 1753–1761 (2013)

    Article  Google Scholar 

  32. H. Zhao, Global asymptotic stability of Hopfield neural network involving distributed delays. IEEE Trans. Neural Netw. 17(1), 47–53 (2004)

    Article  MATH  Google Scholar 

  33. H. Zhao, N. Ding, Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays. Appl Math. Comput. 183(1), 464–470 (2006)

    MathSciNet  MATH  Google Scholar 

  34. H. Zhao, X. Huang, X. Zhang, Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms. Phys. A Stat. Mech. Appl. 421, 300–315 (2015)

    Article  MathSciNet  Google Scholar 

  35. H. Zhao, J. Yuan, X. Zhang, Stability and bifurcation analysis of reaction–diffusion neural networks with delays. Neurocomputing 147, 280–290 (2015)

    Article  Google Scholar 

Download references

Acknowledgments

The work is supported by National Natural Science Foundation of China under Grants 61174155, 61403193 and Qing Lan Project to Jiangsu. The authors would also like to express our gratitude to Editor and the anonymous referees for their valuable comments and suggestions that led to truly significant improvement of the manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Chunlin Sha & Hongyong Zhao

  2. Texas A&M University at Qatar, 5825, Doha, Qatar

    Tingwen Huang

  3. Department of Electronic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Wen Hu

Authors
  1. Chunlin Sha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongyong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tingwen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wen Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongyong Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sha, C., Zhao, H., Huang, T. et al. A Projection Neural Network with Time Delays for Solving Linear Variational Inequality Problems and Its Applications. Circuits Syst Signal Process 35, 2789–2809 (2016). https://doi.org/10.1007/s00034-015-0176-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0176-4

Keywords

Search

Navigation