A dynamic system model for solving convex nonlinear optimization problems

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 4, 2012, Pages 1696-1705

  Nazemi, A R ^a  

^a SHAHROOD UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Convergent; Convex programming; Neural network; Stability

Indexed keywords

CONVEX OPTIMIZATION; NEURAL NETWORKS;

CONSTRAINT FUNCTIONS; CONVERGENT; CONVEX NONLINEAR PROGRAMMING; DYNAMIC SYSTEM MODELS; NEURAL NETWORK MODEL; NEURAL-NETWORKS; NONLINEAR OPTIMIZATION PROBLEMS; NONLINEAR PROGRAMMING PROBLEM; OBJECTIVE FUNCTIONS; STRICTLY CONVEXES;

NONLINEAR PROGRAMMING;

EID: 80054971665     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.08.035     Document Type: Article

References (27)

1. Avriel M. Nonlinear programming: analysis and methods 1976, Prentice-Hall, Englewood Cliffs, NJ.
2. Bazaraa M.S., Sherali H.D., Shetty C.M. Nonlinear programming - theory and algorithms 1993, Wiley, New York. 2nd ed.
3. Fletcher R. Practical methods of optimization 1981, Wiley, New York.
4. He B.S., Zhou J. A modified alternating direction method for convex minimization problems. Appl Math Lett 2000, 13:123-130.
5. Agrawal S.K., Fabien B.C. Optimization of dynamic systems 1999, Kluwer Academic Publishers, Netherlands.
6. Liao L., Qi H., Qi L. Solving nonlinear complementarity problems with neural networks: a reformulation method approach. J Comput Appl Math 2001, 131:343-359.
7. Effati S., Ghomashi A., Nazemi A.R. Application of projection neural network in solving convex programming problems. Appl Math Comput 2007, 188:1103-1114.
8. Effati S., Nazemi A.R. Neural network models and its application for solving linear and quadratic programming problems. Appl Math Comput 2006, 172:305-331.
9. Gao X. A novel neural network for nonlinear convex programming. IEEE Trans Neural Netw 2004, 15:613-621.
10. Hu X., Wang J. Design of general projection neural network for solving monotonoe linear variational inequalities and linear and quadratic programming problems. IEEE Trans Syst Man Cybernet Part B: Cybernet 2007, 37:1414-1421.
11. Kennedy M.P., Chua L.O. Neural networks for nonlinear programming. IEEE Trans Circuits Syst 1988, 35:554-562.
12. Leung Y., Chen K., Gao X. A high-performance feedback neural network for solving convex nonlinear programming problems. IEEE Trans Neural Netw 2003, 14:1469-1477.
13. Liang X.B., Wang J. A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bounded constraints. IEEE Trans Neural Netw 2000, 11:1251-1262.
14. X. Hu, P. Balasubramaniam, Recurrent neural networks, ISBN: 978-953-7619-08-4, pp. 255-388, 2008, I-Tech, Vienna, Austria.
15. Huang Y.C. A novel method to handle inequality constraints for convex programming neural network. Neural Process Lett 2002, 16:17-27.
16. Malek A., Hosseinipour-Mahani N., Ezazipour S. Efficient recurrent neural network model for the solution of general nonlinear optimization problems. Opt Methods Softw 2009, 25:1-18.
17. Popescua M., Dumitracheb A. Stabilization of feedback control and stabilizability optimal solution for nonlinear quadratic problems. Commun Nonlinear Sci Numer Simul 2011, 16:2319-2327.
18. Xia Y., Wang J. A general methodology for designing globally convergent optimization neural networks. IEEE Trans Neural Netw 1998, 9:1331-1343.
19. Xia Y., Wang J. A general projection neural network for solving monotone variational inequality and related optimization problems. IEEE Trans Neural Netw 2004, 15:318-328.
20. Xia Y., Wang J. A recurrent neural network for solving linear projection equations. Neural Netw 2000, 13:337-350.
21. Xia Y., Feng G. A new neural network for solving nonlinear projection equations. Neural Netw 2007, 20:577-589.
22. Xia Y., Leng H., Wang J. A projection neural network and its application to constrained optimization problems. IEEE Trans Circuits Syst 2002, 49:447-458.
23. Xia Y., Wang J. A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints. IEEE Trans Circuits Syst 2004, 51:447-458.
24. Yang Y., Xu X. The projection neural network for solving convex nonlinear programming. ICIC 2007, LNAI 2007, vol. 4682. Springer-Verlag, Heidelberg, p. 174-81.
25. Yang Y., Cao J. A feedback neural network for solving convex constraint optimization problems. Appl Math Comput 2008, 201:340-350.
26. Ortega T.M., Rheinboldt W.C. Iterative solution of nonlinear equations in several variables 1970, Academic, New York.
27. Miller R.K., Michel A.N. Ordinary differential equations 1982, Academic Press, New York.