Noor, M. A.; Al-Said, E. A. Wiener-Hopf equations technique for quasimonotone variational inequalities. (English) Zbl 0953.65050 J. Optimization Theory Appl. 103, No. 3, 705-714 (1999). 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) Cited in 12 Documents 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) Keywords:quasimonotone variational inequalities; Wiener-Hopf equations; algorithms; convergence PDFBibTeX XMLCite \textit{M. A. Noor} and \textit{E. A. Al-Said}, J. Optim. Theory Appl. 103, No. 3, 705--714 (1999; Zbl 0953.65050) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.