A neural network for a class of convex quadratic minimax problems with constraints

IEEE Transactions on Neural Networks

Volumn 15, Issue 3, 2004, Pages 622-628

  Gao, Xing Bao ^a   Liao, Li Zhi ^b   Xue, Weimin ^b  

^a SHAANXI NORMAL UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Convergence and stability; Minimax problem; Neural network; Saddle point

Indexed keywords

ASYMPTOTIC STABILITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING; SYSTEM STABILITY;

EXPONENTIAL STABILITY; MINIMAX PROBLEMS; SADDLE POINT;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK;

NEURAL NETWORKS (COMPUTER);

EID: 2542622863     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2004.824405     Document Type: Article

References (19)

1. M. Avriel, Nonlinear Programming: Analysis and Methods. Englewood Cliffs, NJ: Prentice-Hall, 1976.
2. A. Bouzerdorm and T. R. Pattison, "Neural network for quadratic optimization with bound constraints," IEEE Trans. Neural Networks, vol. 4, pp. 293-304, Mar. 1993.
3. T. L. Friesz, D. H. Bernstein, N. J. Mehta, R. L. Tobin, and S. Ganjlizadeh, "Day-to-day dynamic network disequilibria and idealized traveler information systems," Oper. Res., vol. 42, pp. 1120-1136, 1994.
4. M. Fukushima, "Equivalent differentiable optimization problems and descent method for asymmetric variational inequality problems," Math. Programming, vol. 53, pp. 99-110, 1992.
5. X. B. Gao, "Exponential stability of globally projected dynamic systems," IEEE Trans. Neural Networks, vol. 14, pp. 426-431, Mar. 2003.
6. X. B. Gao and L.-Z. Liao, "A neural network for monotone variational inequalities with linear constraints," Phys. Lett. A, vol. 307, no. 2-3, pp. 118-128, 2003.
7. Q. M. Han, L.-Z. Liao, H. D. Qi, and L. Q. Qi, "Stability analysis of gradient-based neural networks for optimization problems," J. Global Optim., vol. 19, no. 1, pp. 363-381, 2001.
8. B. S. He, "Solution and application of a class of general linear variational inequalities," Sci. China, Ser. A, vol. 39, pp. 395-404, 1996.
9. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. New York: Academic, 1980.
10. L.-Z. Liao and H. D. Qi, "A neural network for the linear complementarity problem," Math. Comput. Model., vol. 29, no. 3, pp. 9-18, 1999.
11. L.-Z. Liao, H. D. Qi, and L. Q. Qi, "Solving nonlinear complementarity problems with neural networks: A reformulation method approach," J. Comput. Appl. Math., vol. 131, no. 1-2, pp. 343-359, 2001.
12. R. T. Rockafellar, "Linear-quadratic programming and optimal control," SIAM J. Control Optim., vol. 25, no. 3, pp. 781-814, 1987.
13. J.-J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
14. Q. Tao and T. J. Fang, "The neural network model for solving minimax problems with constraints" (in Chinese), Control Theory Applicat., vol. 17, no. 1, pp. 82-84, 2000.
15. Y. S. Xia, "A new neural network for solving linear programming and quadratic programming problems," IEEE Trans. Neural Networks, vol. 7, pp. 1544-1547, Nov. 1996.
16. Y. S. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Trans. Neural Networks, vol. 9, pp. 1311-1343, Nov. 1998.
17. ____, "On the stability of globally projected dynamical systems," J. Optim. Theory Appl., vol. 106, no. 1, pp. 129-150, 2000.
18. ____, "A recurrent neural network for solving linear projection equations," Neural Network, vol. 13, pp. 337-350, 2000.
19. ____, "Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights," IEEE Trans. Automat. Contr., vol. 46, pp. 635-638, Apr. 2001.