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Wiener-Hopf equations and variational inequalities. (English) Zbl 0799.49010

Summary: We show that the general variational inequality problem is equivalent to solving the Wiener-Hopf equations. We use this equivalence to suggest and analyze a number of iterative algorithms for solving general variational inequalities. We also discuss the convergence criteria for these algorithms.

MSC:

49J40 Variational inequalities
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[1] Stampacchia, G.,Formes Bilinéaires Coercitives sur les Ensembles Convexes, Comptes Rendus de l’Academie des Sciences, Paris, Vol. 258, pp. 4413-4416, 1964. · Zbl 0124.06401
[2] Kinderlehrer, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980. · Zbl 0457.35001
[3] Baiocchi, C., andCapelo, A.,Variational and Quasi-Variational Inequalities, John Wiley and Sons, New York, New York, 1984.
[4] Kikuchi, N., andOden, J. T.,Contact Problems in Elasticity, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1988. · Zbl 0685.73002
[5] Cottle, R. W., Giannessi, F., andLions, J. L.,Variational Inequalities and Complementary Problems, John Wiley and Sons, New York, New York, 1980.
[6] Glowinski, R., Lions, J. L., andTremolieres, R.,Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, Holland, 1981. · Zbl 0463.65046
[7] Crank, J.,Free and Moving Boundary Problems, Clarendon Press, Oxford, England, 1984. · Zbl 0547.35001
[8] Noor, M. A.,General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119-122, 1988. · Zbl 0655.49005
[9] Noor, M. A.,General Algorithm and Sensitivity Analysis for Variational Inequalities, Journal of Applied Mathematics and Stochastic Analysis, Vol. 5, pp. 29-42, 1992. · Zbl 0749.49010
[10] Speck, F. O.,General Wiener-Hopf Factorization Methods, Pitman Advanced Publishing Program, London, England, 1985. · Zbl 0588.35090
[11] Filippov, V. M.,Variational Principles for Nonpotential Operators, American Mathematical Society Translations, Vol. 77, 1989. · Zbl 0682.35006
[12] Noor, M. A.,General Nonlinear Complementarity Problems, G. Bernhard Riemann: A Mathematical Legacy, Edited by T. M. Rassias and H. M. Srivastava, Hadronic Press, Palm Harbor, Florida, 1994.
[13] Harker, P. T., andPang, J. S.,Finite-Dimensional Variational Inequalities and Nonlinear Complementarity Problems; A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990. · Zbl 0734.90098
[14] Shi, P.,Equivalence of Variational Inequalities with Wiener-Hopf Equations, Proceedings of the American Mathematical Society, Vol. 111, pp. 339-346, 1991. · Zbl 0881.35049
[15] Shi, P.,An Iterative Method for Obstacle Problems via Green’s Function, Nonlinear Analysis: Theory, Methods and Applications, Vol. 15, pp. 339-344, 1990. · Zbl 0725.65068
[16] Noor, M. A.,Iterative Algorithms for Quasi-Variational Inequalities, Pan American Mathematical Journal, Vol. 2, pp. 17-26, 1992. · Zbl 0842.49012
[17] Pitonyak, A., Shi, P., andShillor, M.,On an Iterative Method for Variational Inequalities, Numerische Mathematische, Vol. 58, pp. 231-242, 1990. · Zbl 0689.65043
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