Some iterative methods for general nonconvex variational inequalities

Mathematical and Computer Modelling

Volumn 54, Issue 11-12, 2011, Pages 2955-2961

  Noor, Muhammad Aslam ^a,b  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

^b KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Convergence; Iterative method; Monotone operators; Nonconvex sets; Variational inequalities

Indexed keywords

CONVERGENCE; MONOTONE OPERATORS; MONOTONICITY; NONCONVEX; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

ITERATIVE METHODS;

EID: 80052608659     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.07.017     Document Type: Article

References (30)

1. Noor M.A. General variational inequalities. Appl. Math. Lett. 1988, 1:119-121.
2. Stampacchia G. Formes bilineaires coercitives sur les ensembles convexes. C. R. Math. Acad. Sci. Paris 1964, 258:4413-4416.
3. Bnouhachem A., Noor M.A. Numerical methods for general mixed variational inequalities. J. Appl. Math. Comput. 2008, 204:27-36.
4. Bnouhachem A., Noor M.A. Numerical comparison between prediction-correction methods for general variational inequalities. J. Appl. Math. Comput. 2007, 186:496-505.
5. Bnouhachem A., Noor M.A. Inexact proximal point method for general variational inequalities. J. Math. Anal. Appl. 2006, 324:1195-1212.
6. Bounkhel M., Tadj L., Hamdi A. Iterative schemes to solve nonconvex variational problems. J. Inequal. Pure Appl. Math. 2003, 4:1-14.
7. Clarke F.H., Ledyaev Y.S., Wolenski P.R. Nonsmooth Analysis and Control Theory 1998, Springer-Verlag, Berlin.
8. Kinderlehrer D., Stampacchia G. An Introduction to Variational Inequalities and their Applications 2000, SIAM, Philadelphia.
9. Korpelevich G.M. An extragradient method for finding saddle points and for other problems. Eckonomaki i Mat. Met. 1976, 12:747-756.
10. Noor M.A. Wiener-Hopf equations and variational inequalities. J. Optim. Theory Appl. 1993, 79:197-206.
11. Noor M.A. New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 2000, 251:217-229.
12. Noor M.A. New extragradient-type methods for general variational inequalities. J. Math. Anal. Appl. 2003, 277:379-395.
13. Noor M.A. Some developments in general variational inequalities. Appl. Math. Comput. 2004, 152:199-277.
14. Noor M.A. Iterative schemes for nonconvex variational inequalities. J. Optim. Theory Appl. 2004, 121:385-395.
15. Noor M.A. Merit functions for general variational inequalities. J. Math. Anal. Appl. 2006, 316:736-752.
16. Noor M.A. Differentiable nonconvex functions and general variational inequalities. Appl. Math. Comput. 2008, 199:623-630.
17. Noor M.A. Some iterative methods for general nonconvex variational inequalities. Comput. Math. Model. 2010, 21:87-96.
18. Noor M.A. Some classes of general nonconvex variational inequalities. Albanian J. Math. 2009, 3:175-188.
19. Noor M.A. Nonconvex quasi variational inequalities. J. Adv. Math. Stud. 2010, 3:59-72.
20. Noor M.A. Auxiliary principle technique for solving general mixed variational inequalities. J. Adv. Math. Stud. 2010, 3:89-96.
21. Noor M.A. Projection methods for nonconvex variational inequalities. Optim. Lett. 2009, 3:411-418.
22. Noor M.A. Implicit iterative methods for nonconvex variational inequalities. J. Optim. Theory Appl. 2009, 143:619-624.
23. Noor M.A. Iterative methods for general nonconvex variational inequalities. Albanian J. Math. 2009, 3:117-127.
24. Noor M.A. Principles of Variational Inequalities 2009, Lap-Lambert Academic Publishing AG & Co, Saarbrucken, Germany.
25. Noor M.A. An extragradient algorithm for solving general nonconvex variational inequalities. Appl. Math. Lett. 2010, 23:917-921.
26. Noor M.A. On an implicit method for nonconvex variational inequalities. J. Optim. Theory Appl. 2010, 147:411-417.
27. Noor M.A., Noor K.I., Rassias T.M. Some aspects of variational inequalities. J. Comput. Appl. Math. 1993, 47:285-312.
28. Noor M.A., Rassias Th.M. On nonconvex equilibrium problems. J. Math. Anal. Appl. 2005, 312:289-299.
29. Pang L.P., Shen J., Song H.S. A modified predictor-corrector algorithm for solving nonconvex generalized variational inequalities. Comput. Math. Appl. 2007, 54:319-325.
30. Poliquin R.A., Rockafellar R.T., Thibault L. Local differentiability of distance functions. Trans. Amer. Math. Soc. 2000, 352:5231-5249.