Abstract
By selecting an appropriate transformation of the variables in quadratic programming problems with equality constraints , a lower order recurrent neural network for solving higher quadratic programming is presented. The proposed recurrent neural network is globally exponential stability and converges to the optimal solutions of the higher quadratic programming. An op-amp based on the analogue circuit realization of the recurrent neural network is described. The recurrent neural network proposed in the paper is simple in structure, and is more stable and more accuracy for solving the higher quadratic programming than some existed conclusions, especially for the case that the number of decision variables is close to the number of the constraints. An illustrative example is discussed to show us how to design the analogue neural network using the steps proposed in this paper.
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
Fletcher, M.: Practical Methods of Optimization. John Wiley & Sons, Chichester (1981)
Hopfield, J.J., Tank, D.W.: Neural Computation of Decisions in Optimal Problems. Biological Cybernetics 52(3), 141–152 (1985)
Kennedy, M., Chua, L.O.: Neural Networks for Nonlinear Programming. IEEE Trans., CAS-35(5), 554–562 (1988)
Cheng, L. Hou, Z.-G., Tan, M., Wang, X.: A simplified recurrent neural network for solving nonlinear variational inequalities. In: Proceedings of International Joint Conference on Neural Networks, pp. 104-109 (2008)
Wang, J.: Recurrent Neural Network for Solving Quadtratic Propramming Problems with Equality Constraints. Electronics Letter 28(14), 1345–1347 (1992)
Wang, J.: Primal and Dual Neural Networks for Shortest-path Routing. IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans 28(6), 864–869 (1998)
Xia, Y., Wang, J.: Recurrent Neural Networks for Solving Nonlinear Convex Programs with Linear Constraints. IEEE Transactions on Neural Networks 16(2), 379–386 (2005)
Liao, W., Wang, D., Wang, Z., Liao, X.: Stability of Stochastic Cellular Neural Networks. Journal of Huazhong Univ. of Sci. and Tech. 35(1), 32–34 (2007)
Liao, W., Liao, X., Shen, Y.: Robust Stability of Time-delyed Interval CNN in Noisy Environment. Acta Automatica Sinica 30(2), 300–305 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sun, Y. (2009). A Revised Neural Network for Solving Quadratic Programming Problems. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01513-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-01513-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01512-0
Online ISBN: 978-3-642-01513-7
eBook Packages: Computer ScienceComputer Science (R0)