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Wiener-Hopf equations technique for quasimonotone variational inequalities. (English) Zbl 0953.65050
A general kind of variational inequalities are considered. It is demonstrated that they are equivalent to general Wiener-Hopf equations. Moreover, some new algorithms to solve the general variational inequalities are introduced and their convergence is proved.
Reviewer: V.Arnăutu (Iaşi)

MSC:
65K10 Numerical optimization and variational techniques
49M30 Other numerical methods in calculus of variations (MSC2010)
49J40 Variational inequalities
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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[1] Noor, M. A., General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119–121. 1988. · Zbl 0655.49005
[2] Noor, M. A., Wiener-Hopf Equations and Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 79, pp. 197–206, 1993. · Zbl 0799.49010
[3] Noor, M. A., Some Recent Advances in Variational Inequalities, Part 1: Basic Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 53–80, 1997. · Zbl 0886.49004
[4] Noor, M. A., Some Recent Advances in Variational Inequalities, Part 2: Other Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 229–255, 1997. · Zbl 0889.49006
[5] Noor, M. A., Some Iterative Techniques for General Monotone Variational Inequalities, Optimization, 1999. · Zbl 0966.49010
[6] Noor, M. A., A Modified Extragradient Method for General Monotone Variational Inequalities, Computer Mathematics with Applications, Vol. 38, pp. 19–24, 1999. · Zbl 0939.47055
[7] Noor, M. A., Noor, K. I., and Rassias, T. M., Some Aspects of Variational Inequalities, Journal of Computational and Applied Mathematics, Vol. 47, pp. 285–312, 1993. · Zbl 0788.65074
[8] He, B., A Class of Projection and Contraction Methods for Monotone Variational Inequalities, Applied Mathematics and Optimization, Vol. 35, pp. 69–76, 1997. · Zbl 0865.90119
[9] Solodov, M. V., and Tseng, P., Modified Projection-Type Methods for Monotone Variational Inequalities, SIAM Journal on Control and Optimization, Vol. 34, pp. 1814–1836, 1996. · Zbl 0866.49018
[10] Tseng, P., A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings, SIAM Journal of Control and Optimization, 1999. · Zbl 0997.90062
[11] Stampacchia, G., Formes Bilinearires Coercitives sur les Ensembles Convexes, Comptes Rendus de l’Academie des Sciences, Paris, Vol. 258, pp. 4413–4416, 1964. · Zbl 0124.06401
[12] Baiocchi, C., and Capelo, A., Variational and Quasi-Variational Inequalities, John Wiley and Sons, New York, New York, 1984. · Zbl 0551.49007
[13] Cottle, R. W., Giannessi, F., and Lions, J. L., Variational Inequalities and Complementarity Problems: Theory and Applications, John Wiley and Sons, New York, New York, 1980.
[14] Giannessi, F., and Maugeri, A., Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, New York, 1995. · Zbl 0834.00044
[15] Glowinski, R., Lions, J. L., and TremoliÈres, R., Numerical Analysis of Variational Inequalities, North Holland, Amsterdam, Holland, 1981.
[16] Glowinski, R., Numerical Methods for Nonlinear Variational Problems, North Holland, Amsterdam, Holland, 1984. · Zbl 0536.65054
[17] Noor, M. A., Some Algorithms for General Monotone Mixed Variational Inequalities, Mathematical and Computer Modelling, Vol. 29, pp. 1–9, 1999. · Zbl 0991.49004
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