Abstract
In this paper, a Hopfiled neural network for nonlinear constrained optimization problem is discussed. The energy function for the nonlinear neural network with its neural dynamics is defined based on penalty function with two-order continuous differential. The system of the neural network is stable, and its equilibrium point of the neural dynamics is also an approximately solution for nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is illustrated with the numerical examples.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Hopfield, J.J., Tank, D.W.: Neural Computation of Decision in Optimization Problems. Biological Cybernetics 58, 67–70 (1985)
Joya, G., Atencia, M.A., Sandoval, F.: Hopfield Neural Networks for Optimizatiom: Study of the Different Dynamics. Neurocomputing 43, 219–237 (2002)
Chen, Y.H., Fang, S.C.: Solving Convex Programming Problems with Equality Constraints by Neural Networks. Computers Math. Applic. 36, 41–68 (1998)
Staoshi, M.: Optimal Hopfield Network for Combinatorial Optimization with Linear Cost Function. IEEE Tans. On Neural Networks 9, 1319–1329 (1998)
Xia, Y.S., Wang, J.: A General Methodology for Designing Globally Convergent Optimization Neural Networks. IEEE Trans. On Neural Networks 9, 1331–1444 (1998)
Zenios, S.A., Pinar, M.C., Dembo, R.S.: A Smooth Penalty Function Algorithm for Network-structured Problems. European J. of Oper. Res. 64, 258–277 (1993)
Meng, Z.Q., Dang, C.Y., Zhou, G., Zhu, Y., Jiang, M.: A New Neural Network for Nonlinear Constrained Optimization Problems. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 406–411. Springer, Heidelberg (2004)
Yang, X.Q., Meng, Z.Q., Huang, X.X., Pong, G.T.Y.: Smoothing Nonlinear Penalty Functions for Constrained Optimization. Numerical Functional Analysis Optimization 24, 351–364 (2003)
Lasserre, J.B.: A Globally Convergent Algorithm for Exact Penalty Functions. European Journal of Opterational Research 7, 389–395 (1981)
Fang, S.C., Rajasekera, J.R., Tsao, H.S.J.: Entropy Optimization and Mathematical Proggramming. Kluwer, Dordrecht (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meng, Z., Dang, C. (2005). A Hopfiled Neural Network for Nonlinear Constrained Optimization Problems Based on Penalty Function. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_114
Download citation
DOI: https://doi.org/10.1007/11427391_114
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
Online ISBN: 978-3-540-32065-4
eBook Packages: Computer ScienceComputer Science (R0)