Recurrent neural networks for solving linear inequalities and equations

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 46, Issue 4, 1999, Pages 452-462

  Xia, Youshen ^a   Wang, Jun ^b   Hung, Donald L ^a,b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Linear equalities and equations; Recurrent neural networks

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; PROBLEM SOLVING;

LINEAR EQUALITIES AND EQUATIONS;

RECURRENT NEURAL NETWORKS;

EID: 0033279683     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.754846     Document Type: Article

References (24)

1. D. Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming: Algorithms and Complexity. Boston, MA: Kluwer, 1994. [2] S. Agmon, "The relaxation method for linear inequalities," Canadian J. Math., vol. 6, pp. 382-392, 1954.
2. Y. Censor and T. Elfving, "New method for linear inequalities," Linear Alg. Appl., vol. 42, pp. 199-211, 1982. [4] A. R. De Pierro and A. N. lusem, "A simultaneous projections method for linear inequalities," Linear Alg. Appl., vol. 64, pp. 243-253, 1985.
3. Y. Censor, "Row action techniques for huge and sparse systems and their applications," SIAM Rev., vol. 23, pp. 444-166, 1980.
4. R. Bramley and B. Winnicka, "Solving linear inequalities in a least squares sense," SIAM J. Sei. Comput., vol. 17, no. 1, pp. 287-303, 1996.
5. D. W. Tank and J. J. Hopfield, "Simple 'neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. 33, pp. 533-541, 1986.
6. M. P. Kennedy and L. O. Chua, "Neural networks for nonlinear programming," IEEE Trans. Circuits Syst., vol. 35, pp. 554-562, 1988.
7. A. Rodriguez-Vâzquez, R. Domi'nguez-Castro, A. Rueda, J. L. Huertas, and E. Sânchez-Sinencio, "Nonlinear switched-capacitor 'neural networks' for optimization problems," IEEE Trans. Circuits Syst., vol. 37, pp. 384-397, 1990.
8. C. Y. Maa and M. A. Shanblatt, "Linear and quadratic programming neural network analysis," IEEE Trans. Neural Networks, vol. 3, pp. 580-594, 1992.
9. J. Wang, "Analysis and design of a recurrent neural network for linear programming," IEEE Trans. Circuits Cyst. I, vol. 40, pp. 613-618, 1993.
10. J. Wang, "A deterministic annealing neural network for convex programming," Neural Networks, vol. 7, no. 4, pp. 629-641, 1994.
11. Y. Xia and J. Wang, "Neural network for solving linear programming problems with bounded variables," IEEE Trans. Neural Networks, vol. 6, pp. 515-519, 1995.
12. Y. Xia, "A new neural network for solving linear programming problems and its applications," IEEE Trans. Neural Networks, vol. 7, pp. 525-529, 1996.
13. _, "A new neural network for solving linear and quadratic programming problems," IEEE Trans. Neural Networks, vol. 7, pp. 1544-1547, 1996.
14. A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing. London, U.K.: Wiley, 1993.
15. _, "Neural networks for solving systems of linear equations and related problems," IEEE Trans. Circuits Syst., vol. 39, pp. 124-138, 1992.
16. _, "Neural networks for solving systems of linear equations; Part II: Minimax and least absolute value problems," IEEE Trans. Circuits Syst., vol. 39, pp. 619-633, 1992.
17. J. Wang, "Electronic realization of recurrent neural network for solving simultaneous linear equations," Electron. Lett., vol. 28, no. 5, pp. 493-95, 1992.
18. J. Wang and H. Li, "Solving simultaneous linear equations using recurrent neural networks," Inform. Sei., vol. 76, pp. 255-277, 1994.
19. A. Cichocki and A. Bargiela, "Neural networks for solving linear inequalities," Parallel Comput., vol. 22, pp. 1455-1475, 1997.
20. G. Labonte, "On solving systems of linear inequalities with artificial neural networks," IEEE Trans. Neural Networks, vol. 8, pp. 590-600, 1997.
21. J. M. Ortega and W. G. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic, 1970.
22. G. H. Golub and C. F. Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Press, 1996.
23. X. Lu, "An approximate Newton method for linear programming," J. Numer. Comput. Appl., vol. 15, no. 1, 1994.
24. T. H. Corman, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms. New York: McGraw-Hill, 1990, ch. 2.