zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
49J40Variational methods including variational inequalities
References:
[1]Stampacchia, G.,Formes Bilinéaires Coercitives sur les Ensembles Convexes, Comptes Rendus de l’Academie des Sciences, Paris, Vol. 258, pp. 4413-4416, 1964.
[2]Kinderlehrer, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980.
[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.
[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.
[7]Crank, J.,Free and Moving Boundary Problems, Clarendon Press, Oxford, England, 1984.
[8]Noor, M. A.,General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119-122, 1988. · Zbl 0655.49005 · doi:10.1016/0893-9659(88)90054-7
[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 · doi:10.1155/S1048953392000030
[10]Speck, F. O.,General Wiener-Hopf Factorization Methods, Pitman Advanced Publishing Program, London, England, 1985.
[11]Filippov, V. M.,Variational Principles for Nonpotential Operators, American Mathematical Society Translations, Vol. 77, 1989.
[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 · doi:10.1007/BF01582255
[14]Shi, P.,Equivalence of Variational Inequalities with Wiener-Hopf Equations, Proceedings of the American Mathematical Society, Vol. 111, pp. 339-346, 1991. · doi:10.1090/S0002-9939-1991-1037224-3
[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 · doi:10.1016/0362-546X(90)90142-4
[16]Noor, M. A.,Iterative Algorithms for Quasi-Variational Inequalities, Pan American Mathematical Journal, Vol. 2, pp. 17-26, 1992.
[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 · doi:10.1007/BF01385622