A one-layer recurrent neural network for convex programming

Proceedings of the International Joint Conference on Neural Networks

Volumn , Issue , 2008, Pages 83-90

  Liu, Qingshan ^a   Wang, Jun ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE CLASSIFICATION; LINEAR PROGRAMMING; OPTIMIZATION; RECURRENT NEURAL NETWORKS; REINFORCEMENT LEARNING; VEGETATION;

CONVEX PROGRAMMING PROBLEMS; CONVEX PROGRAMMINGS; DECISION VARIABLES; LINEAR EQUALITIES; MILD CONDITIONS; MODEL COMPLEXITIES; NONNEGATIVITY CONSTRAINTS; OPTIMAL SOLUTIONS; OPTIMIZATION PROBLEMS; SIMULATION RESULTS;

NEURAL NETWORKS;

EID: 56349086972     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IJCNN.2008.4633771     Document Type: Conference Paper

References (29)

1. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms (2nd Ed.), New York: John Wiley, 1993.
2. S. J. Wright, Primal-Dual Interior-Point Methods, Philadelphia, PA: SIAM, 1997.
3. D. W. Tank and J. J. Hopfield, "Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Transactions on Circuits and Systems, vol. 33, pp. 533-541, 1986.
4. M. P. Kennedy and L. O. Chua, "Neural networks for nonlinear programming," IEEE Transactions on Circuits and Systems, vol. 35, pp. 554-562, 1988.
5. C. Y. Maa and M. A. Shanblatt, "Linear and quadratic programming neural network analysis," IEEE Transactions on Neural Networks, vol. 3, pp. 580-594, 1992.
6. J. Wang, "Analysis and design of a recurrent neural network for linear programming," IEEE Transactions on Circuits and Systems-I, vol. 40, pp. 613-618, 1993.
7. J. Wang, "A deterministic annealing neural network for convex, programming," Neural Networks, vol. 7, pp. 629-641, 1994.
8. M. Ford and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Transactions on Circuits and Systems-I, vol. 42, pp. 354-366, 1995.
9. Y. Xia, "A new neural network for solving linear and quadratic programming problems," IEEE Transactions on Neural Networks, vol. 7, pp. 1544-1548, 1996.
10. Y. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Transactions on Neural Networks, vol. 9, pp. 1331-1343, 1998.
11. X. B. Liang and J. Wang, "A recurrent neural network for nonlinear optimization with, a continuously differentiable objective function and bound constraints," IEEE Transactions on Neural Networks, vol. 11, pp. 1251-1262, 2000.
12. Q. Tao, J. Cao, M. Xue, and H. Qiao, "A high performance neural network for solving nonlinear programming problems with hybrid constraints," Physics Letters A, vol. 288, pp. 88-94, 2001.
13. Y. Xia, H. Leung, and J. Wang, "A projection, neural network and its application to constrained optimization problems," IEEE Transactions Circuits and Systems-I, vol. 49, pp. 447-458, 2002.
14. Y. Zhang and J. Wang, "A dual neural network for convex quadratic programming subject to linear equality and inequality constraints," Physics Letters A, vol. 298, pp. 271-278, 2002.
15. M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Transactions on Circuits and Systems-I, vol. 51, pp. 1741-1754, 2004.
16. Y. Xia and J. Wang, "A recurrent neural network for solving nonlinear convex, programs subject to linear constraints," IEEE Transactions on Neural Networks, vol. 16, pp. 379-386, 2005.
17. S. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its kWTA application," IEEE Transactions on Neural Networks, vol. 17, pp. 1500-1510, 2006.
18. Y. Yang and J. Cao, "Solving quadratic programming problems by delayed projection neural network," IEEE Transactions on Neural Networks, vol. 17, pp. 1630-1634, 2006.
19. Q. Liu and J. Wang, "A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming," IEEE Transactions on Neural Networks, in press, 2008.
20. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, New York: Academic, 1982.
21. Y. Xia and J. Wang, "A dual neural network for kinematic control of redundant robot manipulators," IEEE Transactions on Systems, Man and Cybernetics-B, vol. 31, pp. 147-154, 2001.
22. F. H. Clarke, Optimization and Nnonsmooth Analysis, New York: Wiley, 1983.
23. J. P. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory, New York: Springer-Verlag, 1984.
24. M. Forti and P. Nistri, "Global convergence of neural networks with discontinuous neuron, activations," IEEE Transactions on Circuits and Systems-I, vol. 50, pp. 1421-1435, 2003.
25. M. Forti, M. Grazzini, P. Nistri, and L. Pancioni, "Generalized lyapunov approach for convergence of neural networks with discontinuous or non-lipschitz activations," Physica D, vol. 214, pp. 88-99, 2006.
26. W. Lu and T. Chen, "Dynamical behaviors of cohen-grossberg neural networks with discontinuous activation functions," Neural Networks, vol. 18, pp. 231-242, 2005.
27. W. Lu and T. Chen, "Dynamical behaviors of delayed neural network systems with discontinuous activation functions," Neural Computation, vol. 18, pp. 683-708, 2006.
28. G. Li, S. Song, C. Wu, and Z. Du, "A neural network model for non-smooth optimization over a compact convex subset," in Proc. 3rd Int. Symposium on Neural Networks, Springer LNCS 3971, pp. 344-349, 2006.
29. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides. Mathematics and Its Applications (Soviet series), Boston: Kluwer Academic Publishers, 1988.