An extragradient algorithm for solving general nonconvex variational inequalities

Applied Mathematics Letters

Volumn 23, Issue 8, 2010, Pages 917-921

  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

VARIATIONAL TECHNIQUES;

CONVERGENCE; EXTRAGRADIENT ALGORITHMS; EXTRAGRADIENT METHODS; MONOTONE OPERATORS; NONCONVEX SETS; PROJECTION OPERATOR; PSEUDOMONOTONICITY; VARIATIONAL INEQUALITIES;

ITERATIVE METHODS;

EID: 79951517041     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.04.011     Document Type: Article

References (17)

1. G. Stampacchia, Formes bilinêaires coercitives sur les ensembles convexes, C. R. Acad. Sci., Paris 258 (1964) 4413-4416.
2. M. Bounkhel, L. Tadji, A. Hamdi, Iterative schemes to solve nonconvex variational problems, J. Inequal. Pure Appl. Math. 4 (2003) 1-14.
3. F. H. Clarke, Y. S. Ledyaev, P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, Berlin, 1998.
4. G. Cristescu, L. Lupsa, Non-connected Convexities and Applications, Kluwer Academic Publishers, Dordrecht, 2002.
5. R. P. Gilbert, P. D. Panagiotopoulos, P. M. Pardalos (Eds.), From Convexity to Nonconvexity, Kluwer Academic Publishers, Dordrecht, 2001.
6. D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, SIAM, Philadelphia, 2000.
7. M. A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119-121.
8. M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput. 152 (2004) 199-277.
9. M. A. Noor, Merit functions for general variational inequalities, J. Math. Anal. Appl. 316 (2006) 736-752. (Pubitemid 43033582)
10. M. A. Noor, Some iterative methods for general nonconvex variational inequalities, Comput. Math. Model. 21 (2010) 92-109.
11. M. A. Noor, Projection methods for nonconvex variational inequalities, Optim. Lett. 3 (2009) 411-418.
12. M. A. Noor, Iterative methods for general nonconvex variational inequalities, Albanian J. Math. 3 (2009) 117-127.
13. M. A. Noor, Nonconvex quasi variational inequalities, J. Adv. Math. Studies 3 (2010) 59-72.
14. M. A. Noor, K. I. Noor, T. M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993) 285-312.
15. M. A. Noor, T. M. Rassias, On nonconvex equilibrium problems, J. Math. Anal. Appl. 312 (2005) 289-299. (Pubitemid 41554738)
16. R. A. Poliquin, R. T. Rockafellar, L. Thibault, Local differentiability of distance functions, Trans. Amer. Math. Soc. 352 (2000) 5231-5249.
17. I. Singer, Duality for Nonconvex Approximation and Optimization, Springer, New York, 2006.