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Implicit iterative methods for nonconvex variational Inequalities. (English) Zbl 1187.90297

Summary: We suggest and analyze an implicit iterative method for solving nonconvex variational inequalities using the technique of the projection operator. We also discuss the convergence of the iterative method under suitable weaker conditions. Our method of proof is very simple as compared with other techniques.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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[1] Stampacchia, G.: Formes bilineaires coercitives sur les ensembles convexes. C.R. Acad. Sci. Paris 258, 4413–4416 (1964) · Zbl 0124.06401
[2] Bounkhel, M., Tadji, L., Hamdi, A.: Iterative schemes to solve nonconvex variational problems. J. Inequal. Pure Appl. Math.4, 1–14 (2003) · Zbl 1045.58014
[3] Clarke, F.H., Ledyaev, Y.S., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Springer, Berlin (1998) · Zbl 1047.49500
[4] Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. SIAM, Philadelphia (2000) · Zbl 0988.49003
[5] Noor, M.A.: General variational inequalities. Appl. Math. Lett. 1, 119–121 (1988) · Zbl 0655.49005
[6] Noor, M.A.: Some developments in general variational inequalities. Appl. Math. Comput. 152, 199–277 (2004) · Zbl 1134.49304
[7] Noor, M.A.: Iterative schemes for nonconvex variational inequalities. J. Optim. Theory Appl. 121, 385–395 (2004) · Zbl 1062.49009
[8] Noor, M.A.: Projection methods for nonconvex variational inequalities. Optim. Lett. (2009) · Zbl 1171.58307
[9] Noor, M.A., Noor, K.I., Rassias, T.M.: Some aspects of variational inequalities. J. Comput. Appl. Math. 47, 285–312 (1993) · Zbl 0788.65074
[10] Poliquin, R.A., Rockafellar, R.T., Thibault, L.: Local differentiability of distance functions. Trans. Am. Math. Soc. 352, 5231–5249 (2000) · Zbl 0960.49018
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