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 AM  Vol.4 No.1 , January 2013
On Implicit Algorithms for Solving Variational Inequalities
Abstract: This paper presents new implicit algorithms for solving the variational inequality and shows that the proposed methods converge under certain conditions. Some special cases are also discussed.
Cite this paper: E. Al-Shemas, "On Implicit Algorithms for Solving Variational Inequalities," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 102-106. doi: 10.4236/am.2013.41018.
References

[1]   G. Stampacchia, “Formes Bilineaires Coercitives Sur Les Ensembles Convexes,” Académie des Sciences de Paris, Vol. 258, 1964, pp. 4413-4416.

[2]   J. L. Lions and G. Stampacchia, “Variational Inequalities,” Communications on Pure and Applied Mathematics, Vol. 20, No. 3, 1967, pp. 493-512. doi:10.1002/cpa.3160200302

[3]   G. M. Korpelevich, “An Extragradient Method for Finding Saddle Points and for Other Problems,” Ekonomika i Matematicheskie Metody, Vol. 12, No. 4, 1976, pp. 747-756.

[4]   M. A. Noor, K. I. Noor and E. Al-Said, “On New Proximal Methods for Solving the Variational Inequalities,” Journal of Applied Mathematics, 2012, pp. 1-7.

[5]   M. A. Noor, K. I. Noor, E. Al-Said and S. Zainab, “Study on Unified Implicit Methods for Solving Variational Inequalities,” International Journal of Physics, Vol. 7, No. 2, 2012, pp. 222-225.

[6]   M. A. Noor, “Some Developments in General Variational Inequalities,” Applied Mathematics and Computation, Vol. 152, No. 1, 2004, pp. 199-277. doi:10.1016/S0096-3003(03)00558-7

[7]   M. A. Noor, K. I. Noor and T. M. Rassias, “Some Aspects of Variational Inequalities,” Journal of Computational and Applied Mathematics, Vol. 47, No. 3, 1993, pp. 285-312.

[8]   D. Kinderlehrer and G. Stampacchia, “An Introduction to Variational Inequalities and Their Applications,” Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2000. doi:10.1137/1.9780898719451

[9]   E. Al-Shemas, “Wiener-Hopf Equations Technique for Multi-Valued General Variational Inequalities,” Journal of Advanced Mathematical Studies, Vol. 2, No. 2, 2009, pp. 01-08.

[10]   E. Al-Shemas and S. Billups, “An Iterative Method for Generalized Set-Valued Nonlinear Mixed Quasi-Variational Inequalities,” Journal of Applied Mathematics, Vol. 170, No. 2, 2004, pp. 423-432. doi:10.1016/j.cam.2004.01.028

[11]   E. Al-Shemas, “Projection Iterative Methods for Multi-Valued General Variational Inequalities,” Applied Mathematics & Information Sciences, Vol. 3, No. 2, 2009, pp. 177-184.

[12]   E. Al-Shemas, “Resolvent Operator Method for General Variational Inclusions,” Journal of Mathematical Inequalities, Vol. 3, No. 3, 2009, pp. 455-462. doi:10.7153/jmi-03-45

 
 
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