A neural network model for quadratic programming with simple upper and lower bounds and its application to linear programming
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.
Key wordsneural network linear programming quadratic programming limit set
Unable to display preview. Download preview PDF.
- 5.Maa, C.Y., & Shanblatt, M.A., (1992). Linear and quadratic programming neural network analysis. IEEE transactions on neural networks, 3, 380–394.Google Scholar
- 6.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.Google Scholar
- 8.Lasalle, (1976). the stability of dynamical systems. J.W.Arrowsmith Ltd.Google Scholar
- 9.Coste, J., et al., (1979). Simple kinetic model of symmetry breaking. Journal of statistical physics, 21, 33–50.Google Scholar
- 10.Arthur, R.M., (1969). Species packing and what interspecies competition minimizes. proceedings of natural academic science, USA, 64, 1369–1371.Google Scholar
- 11.Nemhauser, G.L., (1989). et al. Optimization. North-Holland.Google Scholar
- 12.Karmarkar, N., (1984). A new polynomial time algorithm for linear programming. Combinatoria, 4, 373–395.Google Scholar
- 13.Fletcher, (1980). Practical methods of optimization. Volume 1: Unconstrained optimization. John Wiley & Sons.Google Scholar
- 14.Gill, P., (1981). et al. Practical Optimization. Academic Press.Google Scholar