Global stability of a recurrent neural network for solving pseudomonotone variational inequalities

Proceedings - IEEE International Symposium on Circuits and Systems

Volumn , Issue , 2006, Pages 755-758

  Hu, Xiaolin ^a   Wang, Jun ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; LINEAR MATRIX INEQUALITIES; PARAMETER ESTIMATION; PROBLEM SOLVING;

GLOBAL ASYMPTOTIC STABILITY; MONOTONE VARIATIONAL INEQUALITIES; PSEUDOMONOTONICITY;

RECURRENT NEURAL NETWORKS;

EID: 34547339197     PISSN: 02714310     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. D. Kinderlehrer and G. Stampcchia, An Introduction to Variational Inequalities and Their Applications. New York: Academic, 1980.
2. L. Vandenberghe, B. L. De Moor, and J. Vandewalle, "The generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits," IEEE Trans. Circuits Syst., vol. 36, pp. 1382-1391, Nov. 1989.
3. P. T. Harker and J. S. Pang, "Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications," Math. prog., vol 48, pp. 161-220, 1990.
4. M. V. Solodov and P. Tseng, "Modified projection-type methods for momotone variational inequalities," SIAM J. Control Optim., vol. 2, pp. 1814-1830, 1996.
5. Y. J. Wang, N. H. Xiu and C. Y. Wang, "Unified framework of extragradient-type methods for pseudomonotone variational inequalities," Journal of Optimization Theory and Applications, vol. 111, no. 3, pp. 641-656, Dec. 2001.
6. Y. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Transactions on Neural Networks, vol. 9, no. 6, pp. 1331-1343, 1998.
7. Y. Xia and J. Wang, "Global exponential stability of recurrent neural networks for solving optimization and related problems," IEEE Transactions on Neural Networks, vol. 11, no. 4, pp. 1017-1022, 2000.
8. X. Liang and J. Si, "Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem," IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 349-359, 2001.
9. Y. Xia, H. Leung, and J. Wang, "A projection neural network and its application to contained optimization problems," IEEE Trans. Circuits Syst. - Part I, vol. 49, no. 4, pp. 447-458, 2002.
10. Y. Xia, "Further results on global convergence and stability of globally projected dynamical systems," Journal of Optimization Theory and Applications, vol. 122, no. 3, pp. 627-649, September 2004.
11. Y. Xia and J. Wang, "A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints," IEEE Trans. Circuits Syst. - Part I, vol. 51, no. 7, pp. 1385-1394, 2004.
12. Y. Zhang, S. S. Ge and T. H. Lee, "A unified quadratic-programming- based dynamical system approach to joint torque optimization of physically constrained redundant manipulators," IEEE Transactions on Systems, Man and Cybernetics, Part B, vol. 34, no. 5, pp. 2126-2132, 2004.
13. R. K. Miller and A. N, Michel, Ordinary differential equations. New York: Academic Press, 1982.
14. S. Karamardian and S. Schaible, "Seven kinds of monotone maps," Journal of Optimization Theory and Applications, vol. 66, no. 1, pp. 37-46, 1990.