Abstract
In this paper we put forward a neural network model for quadratic programming problems with simple upper and lower bounds and analyze the properties of solutions obtained by the model. It is shown that linear programming problems can be transferred into such quadratic programming problems and be solved by the model.
This work is supported partly by the National Natural Science Foundation of China(No. 101931209) and by the Hong Kong Baptist College(Proj. No. FRG /93-94/II-05).
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References
Hopfield, J.J. & Tank, D.W., (1985). Neural computation of decision in optimization problems. Biological cybernetics, 52, 141–152.
Tank, D.W., & Hopfield, J.J., (1986). Simple neural optimization networks: An A/D converter, signal decision network and a linear programming circuit. IEEE transactions on circuit and systems, 33, 533–541.
Kennedy, M.P., & Chua, L.O., (1988). Neural networks for nonlinear programming. IEEE transactions on circuit and systems, 35, 554–562.
Bouzerdoum, A., & Pattison, T.R., (1993). Neural network for quadratic optimization with bound constraints. IEEE transactions on neural networks. 4, 293–304.
Maa, C.Y., & Shanblatt, M.A., (1992). Linear and quadratic programming neural network analysis. IEEE transactions on neural networks, 3, 380–394.
Hopfield, J.J., Neurons with graded response have collective computational properties like those of two-state neurons. proceedings of natural academic science, USA, 81, 3088–3092.
Aiger, S.V.B., et al., (1990). A theoretical investigation into the performance of the Hopfield model. IEEE transactions on neural networks, 1, 204–215.
Lasalle, (1976). the stability of dynamical systems. J.W.Arrowsmith Ltd.
Coste, J., et al., (1979). Simple kinetic model of symmetry breaking. Journal of statistical physics, 21, 33–50.
Arthur, R.M., (1969). Species packing and what interspecies competition minimizes. proceedings of natural academic science, USA, 64, 1369–1371.
Nemhauser, G.L., (1989). et al. Optimization. North-Holland.
Karmarkar, N., (1984). A new polynomial time algorithm for linear programming. Combinatoria, 4, 373–395.
Fletcher, (1980). Practical methods of optimization. Volume 1: Unconstrained optimization. John Wiley & Sons.
Gill, P., (1981). et al. Practical Optimization. Academic Press.
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© 1994 Springer-Verlag Berlin Heidelberg
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Zhang, Xs., Zhu, Hc. (1994). A neural network model for quadratic programming with simple upper and lower bounds and its application to linear programming. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_173
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DOI: https://doi.org/10.1007/3-540-58325-4_173
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