Abstract
In this paper, a delayed Lagrangian network is presented for solving quadratic programming problems. Based on some known results, the delay interval is determined to guarantee the asymptotic stability of the delayed neural network at the optimal solution. One simulation example is provided to show the effectiveness of the approach.
This work was supported by the Hong Kong Research Grants Council under Grant CUHK4165/03E, and the National Natural Science Foundation of China under Grant 60574043.
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References
Tank, D.W., Hopfield, J.J.: Simple Neural Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Trans. Circuits and Systems 33, 533–541 (1986)
Kennedy, M.P., Chua, L.O.: Neural Networks for Nonlinear Programming. IEEE Trans. Circuits and Systems 35, 554–562 (1986)
Bouzerdoum, A., Pattison, T.R.: Neural Network for Quadratic Optimization with Bound Constraints. IEEE Trans. Neural Networks 4, 293–304 (1993)
Zhang, S., Constantinides, A.G.: Lagrange Programming Neural Networks. IEEE Trans. Circuits and Systems II 39, 441–452 (1992)
Zhang, S., Zhu, X., Zou, L.H.: Second-order Neural Nets for Constrained Optimization. IEEE Trans. Neural Networks 3, 1021–1024 (1992)
Wang, J.: A Deterministic Annealing Neural Network for Convex Programming. Neural Networks 7, 629–641 (1994)
Wang, J., Hu, Q., Jiang, D.: A Lagrangian Network for Kinematic Control of Redundant Robot Manipulators. IEEE Trans. Neural Networks 10, 1123–1132 (1999)
Xia, Y.: Global Convergence Analysis of Lagrangian Networks. IEEE Trans. Circuits and Systems I 50, 818–822 (2003)
Wang, J.: Primal and Dual Assignment Networks. IEEE Trans. Neural Networks 8, 784–790 (1997)
Wang, J., Xia, Y.: Analysis and Design of Primal-dual Assignment Networks. IEEE Trans. Neural Networks 9, 183–194 (1998)
Xia, Y., Wang, J.: A General Projection Neural Network for Solving Monotone Variational Inequalities and Related Optimization Problems. IEEE Trans. Neural Networks 15, 318–328 (2004)
Chen, Y.H., Fang, S.C.: Neurocomputing with Time Delay Analysis for Solving Convex Quadratic Programming Problems. IEEE Trans. Neural Networks 11, 230–240 (2000)
Mori, T., Fukuma, N., Kuwahara, M.: On an Estimate of the Decay Rate for Stable Linear Delay Systems. Int. J. Control 36, 95–97 (1982)
Mori, T., Kokame, H.: Stability of \(\dot{x}(t)=Ax(t)+Bx(t-\tau)\). IEEE Trans. Automat. Control 34, 460–462 (1989)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, 2nd edn. John Wiley, New York (1993)
Vidyasagar, M.: Nonlinear System Analysis. Prentice Hall, Englewood Cliffs (1993)
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© 2006 Springer-Verlag Berlin Heidelberg
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Liu, Q., Wang, J., Cao, J. (2006). A Delayed Lagrangian Network for Solving Quadratic Programming Problems with Equality Constraints. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_56
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DOI: https://doi.org/10.1007/11759966_56
Publisher Name: Springer, Berlin, Heidelberg
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