New discrete-time recurrent neural network proposal for quadratic optimization with general linear constraints

IEEE Transactions on Neural Networks and Learning Systems

Volumn 24, Issue 2, 2013, Pages 322-328

  Pérez Ilzarbe, María José ^a  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Discrete time; Global convergence; Hybrid constraints; Neural networks; Quadratic optimization

Indexed keywords

NEURAL NETWORKS; OPTIMIZATION;

DISCRETE TIME; DISCRETE TIME RECURRENT NEURAL NETWORK; DUAL THEORY; GLOBAL CONVER-GENCE; HYBRID CONSTRAINTS; LINEAR CONSTRAINTS; QUADRATIC OPTIMIZATION; QUADRATIC PROBLEM;

RECURRENT NEURAL NETWORKS;

ARTIFICIAL NEURAL NETWORK; SYSTEM ANALYSIS; TIME;

NEURAL NETWORKS (COMPUTER); PROGRAMMING, LINEAR; TIME FACTORS;

EID: 84897021284     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2012.2223484     Document Type: Article

References (20)

1. M. S. Bazaraa and C. Shetty, Nonlinear Programming: Theory and Algorithms. New York: Wiley, 1979
2. J. J. Hopfield and D. W. Tank, "'Neural' computation of decision in optimization problems," Biol. Cybern., vol. 52, pp. 141-152, Mar. 1985 (Pubitemid 15007505)
3. S. Sudharsanan and M. Sundareshan, "Exponential stability and systematic synthesis of a neural network for quadratic minimization," Neural Netw., vol. 4, no. 5, pp. 599-613, 1991 (Pubitemid 21710139)
4. A. Bouzerdoum and T. R. Pattison, "Neural network for quadratic optimization with bound constraints," IEEE Trans. Neural Netw., vol. 4, no. 2, pp. 293-304, Mar. 1993 (Pubitemid 23640394)
5. Y. Leung, K.-Z. Chen, Y.-C. Jiao, X.-B. Gao, and K. S. Leung, "A new gradient-based neural network for solving linear and quadratic programming problems," IEEE Trans. Neural Netw., vol. 12, no. 5, pp. 1074-1083, Sep. 2001 (Pubitemid 32981750)
6. Y. Xia, "An extended projection neural network for constrained optimization," Neural Comput., vol. 16, no. 4, pp. 863-883, Apr. 2004 (Pubitemid 38318135)
7. Q. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its KWTA application," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1500-1510, Nov. 2006 (Pubitemid 44824263)
8. 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, vol. 37, no. 5, pp. 1414-1421, Oct. 2007 (Pubitemid 47534605)
9. M. Yashtini and A. Malek, "Solving complementarity and variational inequalities problems using neural networks," Appl. Math. Comput., vol. 190, no. 1, pp. 216-230, Jul. 2007 (Pubitemid 46856656)
10. M. J. Pérez-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)
11. D. Anguita, A. Boni, and S. Ridella, "A digital architecture for support vector machines: Theory, algorithm, and FPGA implementation," IEEE Trans. Neural Netw., vol. 114, no. 5, pp. 993-1009, Sep. 2003
12. M. Yashtini and A. Malek, "A discrete-time neural network for solving nonlinear convex problems with hybrid constraints," Appl. Math. Comput., vol. 195, no. 2, pp. 576-584, Feb. 2008 (Pubitemid 350309638)
13. H. Tang, H. Li, and Z. Yi, "A discrete-time neural network for optimization problems with hybrid constraints," IEEE Trans. Neural Netw., vol. 21, no. 7, pp. 1184-1189, Jul. 2010
14. 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, Oct. 2011
15. F. Ornelas-Tellez, E. N. Sanchez, and A. G. Loukianov, "Discrete-time neural inverse optimal control for nonlinear systems via passivation," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 8, pp. 1327-1339, Aug. 2012
16. C. E. Castañeda and P. Esquível, "Decentralized neural identifier and control for nonlinear systems based on extended Kalman filter," Neural Netw., vol. 31, pp. 81-87, Jul. 2012
17. Y. Xia, C. Sun, and W. X. Zheng, "Discrete-time neural network for fast solving large linear estimation problems and its application to image restoration," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 5, pp. 812-820, May 2012
18. R. Fletcher, Practical Methods of Optimization, 2nd ed. New York: Wiley, 1987
19. K. C. Tan, H. J. 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)
20. A. Greenbaum and G. H. Rodrigue, "Optimal preconditioners of a given sparsity pattern," BIT Numer. Math., vol. 29, no. 4, pp. 610-634, Dec. 1989