Abstract
In this paper, in terms of a linear matrix inequality (LMI), using a delayed Lagrangian network to solve quadratic programming problems, sufficient conditions on delay-dependent and delay-independent are given to guarantee the globally exponential stability of the delayed neural network at the optimal solution. In addition, exponential convergence rate is estimated by the equation in the paper. Furthermore, the results in this paper improved the ones reported in the existing literatures and the proposed sufficient condition can be checked easily by solving LMI. Two simulation examples are provided to show the effectiveness of the approach and applicability of the proposed criteria.
The work was Supported by Natural Science Foundation of China Three Gorges University(No.604114), Natural Science Foundation of Hubei (Nos.2004ABA055, D200613002) and National Natural Science Foundation of China (No.60574025).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Rodriguez-Vazquez, A., Dominguez-Castro, R., Rueda, A., Huertas, J.L., Sanchez-Sinencio, E.: Nonlinear Switched-capacitor Neural Networks for Optimization problems. IEEE Trans. Circuits Syst. 37, 384–397 (1990)
Gafini, E.M., Bertsekas, D.P.: Two Metric Projection Methods for Constraints Optimization. SIAM J. Contr. Optim. 22, 936–964 (1984)
Xia, Y., Wang, J.: Neural Network for Solving Linear Programming Problems with Bounded Variables. IEEE Trans. Neural Networks 6, 515–519 (1995)
Xia, Y.: A New Neural Network for Solving Linear Programming Problems and Its Applications. IEEE Trans. Neural Networks 7, 525–529 (1996)
Xia, Y., Wang, J.: A Recurrent Neural Network for Solving Linear Projection Equations. Neural Network A 13, 337–350 (2000)
Xia, Y., Leng, H., Wang, J.: A Projection Neural Network and Its Application to Constrained Optimization Problems. IEEE Trans. Circuits Syst. 49, 447–458 (2002)
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)
Zhang, S., Constantinides, A.G.: Lagrange Programming Neural Networks. IEEE Trans. Circuits and Systems II 39, 441–452 (1992)
Wang, J., Hu, Q., Jiang, D.: A Lagrangian Network for Kinematic Control of Redundant Robot Manipulators. IEEE Trans. Neural Networks 10, 1123–1132 (1999)
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)
Liu, Q., Wang, J., Cao, J.: A Delayed Lagrangian Network for Solving Quadratic Programming Problems with Equality Constraints. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 369–378. Springer, Heidelberg (2006)
Luenberger, D.G.: Linear and Nonlinear Programming. Addison-Wesley, Reading (1973)
Moon, Y.S., Park, P., Kwon, W.H., Lee, Y.S.: Delay-dependent Robust Stabilization of Uncertain State-delayed Systems. International Journal of Control 74, 1447–1455 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Jiang, M., Fang, S., Shen, Y., Liao, X. (2007). Improved Results on Solving Quadratic Programming Problems with Delayed Neural Network. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-72395-0_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72394-3
Online ISBN: 978-3-540-72395-0
eBook Packages: Computer ScienceComputer Science (R0)