Abstract
Artificial neural network techniques have been introduced into the area of optimization in the recent decade. Some neural network models have been suggested to solve linear and quadratic programming problems. The Kennedy and Chua model[5] is one of these networks. In this paper results about the convergence of the model are obtained. Another related problem is how to choose a parameter value\(\tilde s\) so that the equilibrium point of the network immediately and properly approximates the original solution. Such an estimation for the parameter is given in a closed form when the network is used to solve linear programming.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
J.J. Hopfield. Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons.Proc. Natl. Acad. Sci. USA, 1984, 81: 3088–3092.
J.J. Hopfield and D.D. Tank. “Neural” Computation of Decisions in Optimization Problems.Biological Cybernetics, 1985, 52: 141–152.
D.W. Tank and J.J. Hopfield. Simple Neural Optimization Networks: An A/D Converter, Signal Decision Network, and a Linear Programming Circuit.IEEE Trans. Circuits Syst., 1986, CAS-33: 533–541.
L.O. Chua and G.N. Lin. Nonlinear Programming without Computation.IEEE Trans. Circuits Syst., 1984, CAS-31: 182–188.
M.P. Kennedy and L.O. Chua. Neural Networks for Nonlinear Programming.IEEE Trans. Circuits Syst., 1988, 35: 554–562.
A. Rodriguez-Vazquez et al. Nonlinear Switched-capacitor Neural Networks for Optimization Problems.IEEE Trans. Circuits Syst., 1990, 37: 384–398.
C.Y. Maa and M.A. Shanblatt. A Constrained Optimization Neural Net Technique for Power System Analysis. Proc. IEEE Int. Symp. Circuits Syst., 2946–2950, 1990.
C.Y. Maa and M.A. Shanblatt. Linear and Quadratic Programming Neural Network Analysis.IEEE Trans. Neural Net., 1992, 3: 580–594.
C.Y. Maa and M.A. Shanblatt. A Two-phase Optimization Neural Network.IEEE Trans. Neural Net., 1992, 3: 1003–1009.
A. Cichocki and R. Unbehauen. Switched-capacitor Neural Networks for Differential Optimization.International J. of Circuit Theory and Applications, 1991, 19: 161–187.
Zhang Shengwei and A.G. Constantinides. Lagrange Programming Neural Networks.IEEE Trans. on Neural Networks, 1992, 36: 441–452.
A. Bouzerdoum and T.R. Pattison. Neural Network for Quadratic Optimization with Bound Constraints.IEEE Trans. Neural Net., 1993, 4: 293–304.
Xiang-sun ZHANG and Hui-can ZHU. A Neural Network Model for Quadratic Programming with Simple Upper and Lower Bounds and Its Application to Linear Programming. In: Algorithms and Computation, Lecture Notes in Computer Science, 834: 119–127, Springer-Verlag, Berlin, 1994.
M.S. Bazaraa, C.M. Shetty. Nonlinear Programming: Theory and Algorithms. John Wiley, Sons, Inc., New York, 1979.
Author information
Authors and Affiliations
Additional information
This work is supported by the National Natural Science Foundation of China (No. 69574034) and the Laboratory of Management, Decision and Information System, CAS.
Rights and permissions
About this article
Cite this article
Zhang, X. Mathematical analysis of some neural networks for solving linear and quadratic programming. Acta Mathematicae Applicatae Sinica 12, 1–10 (1996). https://doi.org/10.1007/BF02009555
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02009555