One-layer continuous-and discrete-time projection neural networks for solving variational inequalities and related optimization problems

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 7, 2014, Pages 1308-1318

  Liu, Qingshan ^a   Huang, Tingwen ^b   Wang, Jun ^c,d  

^a SOUTHEAST UNIVERSITY   (China)

^b TEXAS A AND M UNIVERSITY AT QATAR   (Qatar)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^d DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Constrained optimization; global convergence; Lyapunov stability; projection neural network; variational inequalities

Indexed keywords

CONSTRAINED OPTIMIZATION; VARIATIONAL TECHNIQUES;

DESIGN PARAMETERS; GLOBAL CONVER-GENCE; LYAPUNOV STABILITY; MODEL COMPLEXITY; OPTIMIZATION PROBLEMS; PROJECTION NEURAL NETWORK; PROJECTION OPERATOR; VARIATIONAL INEQUALITIES;

NETWORK LAYERS;

EID: 84903309868     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2292893     Document Type: Article

References (40)

1. A. Cochocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing. New York, NY, USA: Wiley, 1993.
2. F. Facchinei and J. Pang, Finite-dimensional Variational Inequalities an Complementarity Problems. New York, NY, USA: Springer-Verlag, 2003.
3. P. Harker and J. Pang, "Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications," Math. Program., vol. 48, no. 1, pp. 161-220, 1990.
4. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. New York, NY, USA: Academic, 1982.
5. Y. Xia and J. Wang, "A one-layer recurrent neural network for support vector machine learning," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 34, no. 2, pp. 1261-1269, Apr. 2004.
6. M. Kennedy and L. Chua, "Neural networks for nonlinear programming," IEEE Trans. Circuits Syst., vol. 35, no. 5, pp. 554-562, May 1988.
7. X. Liang and J. Wang, "A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints," IEEE Trans. Neural Netw., vol. 11, no. 6, pp. 1251-1262, Nov. 2000.
8. Q. Liu and J. Cao, "A recurrent neural network based on projection operator for extended general variational inequalities," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 40, no. 3, pp. 928-938, Jun. 2010.
9. D. Tank and J. Hopfield, "Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. 33, no. 5, pp. 533-541, May 1986. (Pubitemid 16595842)
10. A. Bouzerdoum and T. Pattison, "Neural network for quadratic optimization with bound constraints," IEEE Trans. Neural Netw., vol. 4, no. 2, pp. 293-304, Mar. 1993. (Pubitemid 23640394)
11. E. Chong, S. Hui, and S. Zak, "An analysis of a class of neural networks for solving linear programming problems," IEEE Trans. Autom. Control, vol. 44, no. 11, pp. 1995-2006, Nov. 1999. (Pubitemid 30531636)
12. C. Maa and M. Shanblatt, "Linear and quadratic programming neural network analysis," IEEE Trans. Neural Netw., vol. 3, no. 4, pp. 580-594, Jul. 1992.
13. J. Wang, "Analysis and design of a recurrent neural network for linear programming," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 9, pp. 613-618, Sep. 1993.
14. Y. Xia and J. Wang, "A general projection neural network for solving monotone variational inequalities and related optimization problems," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 318-328, Mar. 2004.
15. J. Wang, "Primal and dual neural networks for shortest-path routing," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 28, no. 6, pp. 864-869, Nov. 1998. (Pubitemid 128748092)
16. J. Wang, "Primal and dual assignment networks," IEEE Trans. Neural Netw., vol. 8, no. 3, pp. 784-790, May 1997. (Pubitemid 127767819)
17. X. Hu and J. Wang, "Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 37, no. 5, pp. 1414-1421, Oct. 2007. (Pubitemid 47534605)
18. Y. Xia and J. Wang, "On the stability of globally projected dynamical systems," J. Optim. Theory Appl., vol. 106, no. 1, pp. 129-150, 2000.
19. Q. Liu, Z. Guo, and J. Wang, "A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization," Neural Netw., vol. 26, pp. 99-109, Feb. 2012.
20. Q. Liu and J.Wang, "A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming," IEEE Trans. Neural Netw., vol. 19, no. 4, pp. 558-570, Apr. 2008. (Pubitemid 351583574)
21. W. Bian and X. Xue, "Subgradient-based neural networks for nonsmooth nonconvex optimization problems," IEEE Trans. Neural Netw., vol. 20, no. 6, pp. 1024-1038, Jun. 2009.
22. Q. Liu and J. Wang, "A one-layer recurrent neural network for constrained nonsmooth optimization," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 41, no. 5, pp. 1323-1333, Oct. 2011.
23. M. Bazaraa, H. Sherali, and C. Shetty, Nonlinear Programming: Theory and Algorithms, 3rd ed. New York, NY, USA: Wiley, 2006.
24. Y. Xia, "An extended projection neural network for constrained optimization," Neural Comput., vol. 16, no. 4, pp. 863-883, 2004. (Pubitemid 38318135)
25. T. Friesz, D. Bernstein, N. Mehta, R. Tobin, and S. Ganjalizadeh, "Day-to-day dynamic network disequilibria and idealized traveler information systems," Oper. Res., vol. 42, no. 6, pp. 1120-1136, 1994.
26. X. Gao and L. Liao, "A new projection-based neural network for constrained variational inequalities," IEEE Trans. Neural Netw., vol. 20, no. 3, pp. 373-388, Mar. 2009.
27. X. Hu and J. Wang, "Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1487-1499, Nov. 2006. (Pubitemid 44824262)
28. X. Hu and J. Wang, "A recurrent neural network for solving a class of general variational inequalities," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 37, no. 3, pp. 528-539, Jun. 2007. (Pubitemid 46784589)
29. Q. Liu and Y. Yang, "Global exponential system of projection neural networks for system of generalized variational inequalities and related nonlinear minimax problems," Neurocomputing, vol. 73, nos. 10-12, pp. 2069-2076, 2010.
30. Q. Liu and J. Wang, "A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints," IEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 5, pp. 812-824, May 2013.
31. Q. Liu and J. Wang, "A one-layer recurrent neural network for non-smooth convex optimization subject to linear equality constraints," in Proc. 15th ICONIP, 2009, pp. 1003-1010.
32. O. Diene and A. Bhaya, "Perceptron training algorithms designed using discrete-time control Liapunov functions," Neurocomputing, vol. 72, nos. 13-15, pp. 3131-3137, 2009.
33. F. A. Pazos, A. Bhaya, and E. Kaszkurewicz, "Design of second order neural networks as dynamical control systems that aim to minimize nonconvex scalar functions," Neurocomputing, vol. 97, pp. 174-191, Nov. 2012.
34. J. LaSalle, The Stability of Dynamical Systems. Philadelphia, PA, USA: SIAM, 1976.
35. S. Boyd, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA, USA: SIAM, 1994.
36. M. Perez-Ilzarbe, "Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1344-1351, Nov. 1998. (Pubitemid 128742413)
37. K. Tan, H. Tang, and Z. Yi, "Global exponential stability of discrete-time neural networks for constrained quadratic optimization," Neurocomputing, vol. 56, pp. 399-406, Jan. 2004. (Pubitemid 38145635)
38. Q. Liu and J. Cao, "Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints," Neurocomputing, vol. 74, no. 17, pp. 3494-3501, 2011.
39. Y. Xia and J. Wang, "A recurrent neural network for solving nonlinear convex programs subject to linear constraints," IEEE Trans. Neural Netw., vol. 16, no. 2, pp. 379-386, Mar. 2005. (Pubitemid 40390821)
40. Y. Xia, G. Feng, and J. Wang, "A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints," IEEE Trans. Neural Netw., vol. 19, no. 8, pp. 1340-1353, Aug. 2008.