A Gradient-Descent Neurodynamic Approach for Distributed Linear Programming

  • Xinrui Jiang
  • Sitian QinEmail author
  • Ping Guo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11555)


In this paper, a gradient-descent neurodynamic approach is proposed for the distributed linear programming problem with affine equality constraints. It is rigorously proved that the state solution of the proposed gradient-descent approach with an arbitrary initial point reaches agreement and is convergent to an optimal solution of the considered optimization problem at the same time. In the end, some numerical experiments are conducted to verify the effectiveness of the proposed gradient-descent approach.


Distributed linear programming Gradient-descent neurodynamic approach Reach agreement Convergence to an optimal solution 



This research is supported by the National Natural Science Foundation of China (61773136, 11471088) and the NSFC and CAS project in China with granted No. U1531242.


  1. 1.
    Balasubramanian, A., Levine, B.N., Venkataramani, A.: DTN routing as a resource allocation problem. ACM SIGCOMM Comput. Commun. Rev. 37(4), 373–384 (2007)Google Scholar
  2. 2.
    Cochocki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing. Wiley, New York (1993)Google Scholar
  3. 3.
    Deng, Z., Liang, S., Hong, Y.: Distributed continuous-time algorithms for resource allocation problems over weight-balanced digraphs. IEEE Trans. Cybern. 48(11), 3116–3125 (2018)Google Scholar
  4. 4.
    Forti, M., Nistri, P., Quincampoix, M.: Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality. IEEE Trans. Neural Netw. Learn. Syst. 17(6), 1471–1486 (2006)Google Scholar
  5. 5.
    Gharesifard, B., Cortes, J.: Distributed continuous-time convex optimization on weight-balanced digraphs. IEEE Trans. Autom. Control 59(3), 781–786 (2012)Google Scholar
  6. 6.
    Hopfield, J., Tank, D.: Neural computation of decisions in optimization problems. Biol. Cybern. 52(3), 141–152 (1985)Google Scholar
  7. 7.
    Kia, S.S., Cortes, J., Martinez, S.: Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication. Automatica 55, 254–264 (2015)Google Scholar
  8. 8.
    Li, G., Song, S., Wu, C., Du, Z.: A neural network model for non-smooth optimization over a compact convex subset. In: Wang, J., Yi, Z., Zurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 344–349. Springer, Heidelberg (2006). Scholar
  9. 9.
    Li, Z., Liu, X., Wei, R., Xie, L.: Distributed tracking control for linear multiagent systems with a leader of bounded unknown input. IEEE Trans. Autom. Control 58(2), 518–523 (2013)Google Scholar
  10. 10.
    Li, Z., Wei, R., Liu, X., Xie, L.: Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica 49(7), 1986–1995 (2013)Google Scholar
  11. 11.
    Liu, N., Qin, S.: A novel neurodynamic approach to constrained complex-variable pseudoconvex optimization. IEEE Trans. Cybern. (2018). Scholar
  12. 12.
    Liu, N., Qin, S.: A neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints. Neural Netw. 109, 147–158 (2019)Google Scholar
  13. 13.
    Liu, Q., Yang, S., Wang, J.: A collective neurodynamic approach to distributed constrained optimization. IEEE Trans. Neural Netw. Learn. Syst. 28(8), 1747–1758 (2017)Google Scholar
  14. 14.
    Ma, K., et al.: Stochastic non-convex ordinal embedding with stabilized Barzilai-Borwein step size. arXiv:1711.06446
  15. 15.
    Min, H., Meng, Z., Zhang, Y.: Projective synchronization between two delayed networks of different sizes with nonidentical nodes and unknown parameters. Neurocomputing 171, 605–614 (2016)Google Scholar
  16. 16.
    Min, H., Zhang, M., Qiu, T., Xu, M.: UCFTS: a unilateral coupling finite-time synchronization scheme for complex networks. IEEE Trans. Neural Netw. Learn. Syst. 30(1), 255–268 (2019)Google Scholar
  17. 17.
    Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54(1), 48–61 (2009)Google Scholar
  18. 18.
    Nedic, A., Ozdaglar, A., Parrilo, P.A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Autom. Control 55(4), 922–938 (2010)Google Scholar
  19. 19.
    Qin, S., Le, X., Wang, J.: A neurodynamic optimization approach to bilevel quadratic programming. IEEE Trans. Neural Netw. Learn. Syst. 28(11), 2580–2591 (2017)Google Scholar
  20. 20.
    Qin, S., Yang, X., Xue, X., Song, J.: A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints. IEEE Trans. Cybern. 47(10), 3063–3074 (2017)Google Scholar
  21. 21.
    Wu, A., Zeng, Z.: Exponential stabilization of memristive neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 23(12), 1919–1929 (2012)Google Scholar
  22. 22.
    Yang, S., Liu, Q., Wang, J.: A multi-agent system with a proportional-integral protocol for distributed constrained optimization. IEEE Trans. Autom. Control 62(7), 3461–3467 (2017)Google Scholar
  23. 23.
    Yi, P., Hong, Y., Liu, F.: Distributed gradient algorithm for constrained optimization with application to load sharing in power systems. Syst. Control Lett. 83(711), 45–52 (2015)Google Scholar
  24. 24.
    You, K., Xie, L.: Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans. Autom. Control 56(10), 2262–2275 (2011)Google Scholar
  25. 25.
    Zhu, Y., Yu, W., Wen, G., Chen, G.: Projected primal-dual dynamics for distributed constrained nonsmooth convex optimization. IEEE Trans. Cybern. (2018).
  26. 26.
    Zhu, Y., Yu, W., Wen, G., Ren, W.: Continuous-time coordination algorithm for distributed convex optimization over weight-unbalanced directed networks. IEEE Trans. Circ. Syst. II Express Briefs (2018).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of MathematicsHarbin Institute of TechnologyWeihaiChina
  3. 3.Laboratory of Image Processing and Pattern RecognitionBeijing Normal UniversityBeijingChina

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