An alternative recurrent neural network for solving variational inequalities and related optimization problems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 39, Issue 6, 2009, Pages 1640-1645

  Hu, Xiaolin ^a   Zhang, Bo ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Asymptotic stability; Global convergence; Linear programming (LP); Optimization; Quadratic programming (QP); Recurrent neural network (RNN); Variational inequality

Indexed keywords

CLASSICAL MODEL; COMPUTING-TASK; DYNAMIC SYSTEMS; GLOBAL CONVERGENCE; NON-LINEAR CONSTRAINTS; OPTIMIZATION PROBLEMS; VARIATIONAL INEQUALITIES; VARIATIONAL INEQUALITY;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; COMPUTER SCIENCE; DYNAMIC PROGRAMMING; DYNAMICAL SYSTEMS; LINEAR PROGRAMMING; LINEARIZATION; OPTIMIZATION; QUADRATIC PROGRAMMING; REINFORCEMENT LEARNING; SYSTEM STABILITY; VARIATIONAL TECHNIQUES;

RECURRENT NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER);

EID: 70349622494     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2009.2025700     Document Type: Article

References (27)

1. Y. Xia, "A new neural network for solving linear and quadratic programming problems," IEEE Trans. Neural Netw., vol. 7, no. 6, pp. 1544-1547, Nov. 1996.
2. Y. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Trans. Neural Netw. vol. 9, no. 6, pp. 1331-1343, Nov. 1998.
3. Q. Tao, J. Cao, and D. Sun, "A simple and high-performance neural network for quadratic programming problems," Appl. Math. Comput., vol. 124, no. 2, pp. 251-260, Nov. 2001.
4. Y. Xia, "An extended projection neural network for constrained optimization," Neural Comput., vol. 16, no. 4, pp. 863-883, Apr. 2004.
5. X. Gao, "A novel neural network for nonlinear convex programming," IEEE Trans. Neural Netw., vol. 15, no. 3, pp. 613-621, May 2004.
6. M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 9, pp. 1741-1754, Sep. 2004.
7. X. Gao, L. Liao, and L. Qi, "A novel neural network for variational inequalities with linear and nonlinear constraints," IEEE Trans. Neural Netw., vol. 16, no. 6, pp. 1305-1317, Nov. 2005.
8. X. Gao and L. Du, "A neural network with finite-time convergence for a class of variational inequalities," in Proc. 4th Int. Conf. Intell. Comput., Kunming, China, Aug. 2006, vol. 4113, pp. 32-41.
9. Y. Yang and J. Cao, "Solving quadratic programming problems by delayed projection neural network," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1630-1634, Nov. 2006.
10. Y. Yang and J. Cao, "A delayed neural network method for solving convex optimization problems," Int. J. Neural Syst., vol. 16, no. 4, pp. 295-303, Aug. 2006.
11. 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.
12. H. Ghasabi-Oskoei and N. Mahdavi-Amiri, "An efficient simplified neural network for solving linear and quadratic programming problems," Appl. Math. Comput., vol. 175, no. 1, pp. 452-464, Apr. 2006.
13. R. Perfetti and E. Ricci, "Analog neural network for support vector machine learning," IEEE Trans. Neural Netw., vol. 17, no. 4, pp. 1085-1091, Jul. 2006.
14. 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.
15. X. Hu and J. Wang, "Solving generally constrained generalized linear variational inequalities using the general projection neural networks," IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1697-1708, Nov. 2007.
16. Y. Xia, G. Feng, and M. Kamel, "Development and analysis of a neural dynamical approach to nonlinear programming problems," IEEE Trans. Autom. Control, vol. 52, no. 11, pp. 2154-2159, Nov. 2007.
17. Y. Xia and G. Feng, "A new neural network for solving nonlinear projection equations," Neural Netw., vol. 20, no. 5, pp. 577-589, Jul. 2007.
18. 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.
19. L. Cheng, Z. G. Hou, and M. Tan, "A neutral-type delayed-projection neural network for solving nonlinear variational inequalities," IEEE Trans. Circuits Syst. II: Exp. Briefs, vol. 55, no. 8, pp. 806-810, Aug. 2008.
20. X. Hu and B. Zhang, "A new recurrent neural network for solving convex quadratic programming problems with an application to the k winnerstake-all problem," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 654-664, Apr. 2009.
21. Y. Xia and M. S. Kamel, "A generalized least absolute deviation method for parameter estimation of autoregressive signals," IEEE Trans. Neural Netw., vol. 19, no. 1, pp. 107-118, Jan. 2008.
22. 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 Trans. Syst., Man, Cybern. B: Cybern., vol. 34, no. 5, pp. 2126-2132, Oct. 2004.
23. Z. Hou, L. Cheng, and M. Tan, "Coordination of two redundant robots using a dual neural network," in Proc. IJCNN, Vancouver, BC, Canada, Jul. 2006, pp. 4187-4192.
24. Z. Hou, M. Gupta, P. Nikiforuk, M. Tan, and L. Cheng, "A recurrent neural network for hierarchical control of interconnected dynamic systems," IEEE Trans. Neural Netw., vol. 18, no. 2, pp. 466-481, Mar. 2007.
25. Y. Pan and J. Wang, "Two neural network approaches to model predictive control," in Proc. Amer. Control Conf., Seattle, WA, Jun. 2008, pp. 1685-1690.
26. F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I/II. New York: Springer-Verlag, 2003.
27. Y. Xia and G. Feng, "On the convergence conditions of an extended projection neural network," Neural Comput., vol. 17, no. 3, pp. 515-525, Mar. 2005.