References

MODIFIED PROXIMAL ALGORITHMS FOR SOLVING VARIATIONAL INEQUALITIES


[1] E. Al-Shemas and Stephen C. Billups, An iterative method for generalized set-valued nonlinear mixed quasi-variational inequalities, J. Comp. Appl. Math. 170(2) (2004), 423-432.

[2] E. Al-Shemas, Wiener-Hopf equations technique for multivalued general variational inequalities, J. Adv. Math. Stud. 2(2) (2009), 01-08.

[3] E. Al-Shemas, Projection iterative methods for multivalued general variational inequalities, Appl. Math. Inform. Sci. 3(2) (2009), 177-184.

[4] E. Al-Shemas, Resolvent operator method for general variational inclusions, J. Math. Inequal. 3(3) (2009), 4554-4562.

[5] A. Auslender, M. Teboulle and S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Comput. Optim. Appl. 12 (1999), 31-40.

[6] C. Baiocchi and A. Capelo, Variational and Quasi-Variational Inequalities: Application to Free-Boundary Problems, Wiley, New York, 1984.

[7] L. Bregman, The relaxation method of finding the common points of convex sets and its applications to the solution of problems in convex programming, USSR Comput. Math. Math. Phys. 7 (1967), 200-217.

[8] R. S. Burachik, Generalized Proximal Point Methods for the Variational Inequality Problem, PhD. Thesis, Instituto de Matemàtica Pura ed Aplcada, Rio de Janeiro, Brazil, 1995.

[9] D. Han and Wenyu Sun, New decomposition methods for solving variational inequality problems, Math. Comput. Modelling 37 (2003), 405-418.

[10] B. S. He and H. Yang, Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities, Oper. Res. Lett. 23 (1998), 151-161.

[11] B. S. He, H. Yang, L. Z. Liao and D. Han, A decomposition method for a class of monotone variational inequality problem, Math. Program. 103(3) (1999), 603-622.

[12] B. S. He, H. Yang, L. Z. Liao and D. Han, A new alternating directions method for monotone variational inequalities, Math. Program. (2001).

[13] A. N. Iusem and M. Teboulle, Convergence analysis of non-quadratic proximal methods for convex and linear programming, Math. Oper. Res. 20(3) (1995), 657-677.

[14] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Application, Academic Press, New York, 1980.

[15] K. C. Kiwiel, Proximal minimization methods with generalized Bregman functions, SIAM J. Control and Optim. 35(4) (1997), 1142-1168.

[16] J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493-519.

[17] P. Marcotte and D. Zhu, Coupling the auxiliary problem principle with descent methods of pseudoconvex programming, European J. Oper. Res. 83 (1995), 670-685.

[18] B. Martinet, Regularization d’inequations variationales par approximations successive, Revue Fran. d’Informat. Rech. Oper. 4 (1970), 154-159.

[19] M. A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988), 119-121.

[20] M. A. Noor, K. I. Noor and Th. M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993), 285-312.

[21] M. A. Noor, Operator-splitting methods for general mixed variational inequalities, J. Inequal. Pure Appl. Math. 3(5) (2002), 1-9.

[22] M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput. 152 (2004), 199-277.

[23] M. A. Noor, Differentiable nonconvex functions and general variational inequalities, Appl. Math. Comput. 199 (2008), 623-630.

[24] M. A. Noor, Extended general variational inequalities, Appl. Math. Lett. 22 (2009), 182-186.

[25] R. Polyak and M. Teboulle, Nonlinear re-scaling and proximal-like methods in convex programming, Math. Program. 76 (1997), 265-284.

[26] R. Polyak, Nonlinear re-scaling multiplier method as interior quadratic prox, Math. Program. (2003).

[27] R. T. Rockafellar, Augmented Lagrangian and applications of the proximal point algorithm in convex programming, Math. Oper. Res. 1 (1976), 97-116.

[28] G. Stampacchia, Formes bilineaires coercivities surles ensembles convex, C. R. Acad. Sci. Paris 258 (1964), 4413-4416.