A novel neural network for a class of convex quadratic minimax problems

Neural Computation

Volumn 18, Issue 8, 2006, Pages 1818-1846

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

^a SHAANXI NORMAL UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745863905     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2006.18.8.1818     Document Type: Article

References (24)

1. Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (1993). Nonlinear programming theory and algorithms (2nd ed.). New York: Wiley.
2. Bouzerdorm, A., & Pattison, T. R. (1993). Neural network for quadratic optimization with bound constraints. IEEE Trans. Neural Networks, 4, 293-304.
3. Friesz, T. L., Bernstein, D. H., Mehta, N. J., Tobin, R. L., & Ganjlizadeh, S. (1994). Day-to-day dynamic network disequilibria and idealized traveler information systems. Operations Research, 42, 1120-1136.
4. Fukushima, M. (1992). Equivalent differentiable optimization problems and descent method for asymmetric variational inequality problems. Mathematical Programming, 53, 99-110.
5. Gao, X. B. (2003). Exponential stability of globally projected dynamic systems. IEEE Trans. Neural Networks, 14, 426-431.
6. Gao X. B. (2004). A novel neural network for nonlinear convex programming. IEEE Trans. Neural Networks, 15, 613-621.
7. Gao, X. B., & Liao, L.-Z. (2003). A neural network for monotone variational inequalities with linear constraints. Physics Letters A, 307, 118-128.
8. Gao, X. B., Liao, L.-Z., & Xue, W. M. (2004). A neural network for a class of convex quadratic minimax problems with constraints. IEEE Trans. Neural Networks, 15, 622-628.
9. Han, Q. M., Liao, L.-Z., Qi, H. D., & Qi, L. Q. (2001). Stability analysis of gradient-based neural networks for optimization problems. J. Global Optim., 19, 363-381.
10. He, B. S. (1996). Solution and application of a class of general linear variational inequalities. Science in China, series A, 39, 395-404.
11. He, B. S. (1999). Inexact implicit methods for monotone general variational inequalities. Mathematical Programming, 86, 199-217.
12. He, B. S., & Yang, H. (2000). A neural-network model for monotone linear asymmetric variational inequalities. IEEE Trans. Neural Networks, 11, 3-16.
13. Kinderlehrer, D., & Stampacchia, G. (1980). An introduction to variational inequalities and their applications. New York: Academic Press.
14. Ortega, T. M., & Rheinboldt, W. C. (1970). Iterative solution of nonlinear equation in several variables. New York: Academic Press.
15. Rockafellar, R. T. (1987). Linear-quadratic programming and optimal control. SIAM J. Control Optim., 25, 781-814.
16. Smith, T. E., Friesz, T. L., Bernstein, D. H., & Suo, Z. G. (1997). A comparative analysis of two minimum-norm projective dynamics and their relationship to variational inequalities. In M. C. Ferris, J. S. Pang (Eds.), Complementarity and variational problems: State of art (pp. 405-424). Philadelphia: SIAM.
17. Solodov, M. V., & Tseng, P. (1996). Modified projection-type methods for monotone variational inequalities. SIAM J. Control Optim., 27, 1814-830.
18. Tseng, P. (2000). A modified forward-backward splitting method for maximal monotone mappings. SIAM J. Control Optim., 38, 431-446.
19. Xia, Y. S. (2004). An extended projection neural network for constrained optimization. Neural Computation, 16, 863-883.
20. Xia, Y. S., & Feng, G. (2004). On convergence rate of projection neural networks. IEEE Trans. Automatic Control, 49, 91-96.
21. Xia, Y. S., Feng, C., & Wang, J. (2004). A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations. Neural Networks, 17, 1003-1015.
22. Xia, Y. S., & Wang, J. (1998). A general methodology for designing globally convergent optimization neural networks. IEEE Trans. Neural Networks, 9, 1331-1343.
23. Xia, Y. S., & Wang, J. (2000). On the stability of globally projected dynamical systems. J. Optim. Theory Appl., 106, 129-160.
24. Xia, Y. S., & Wang, J. (2001). Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights. IEEE Trans. Automatic Control, 46, 635-638.