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)
Auxiliary principle technique for solving bifunction variational inequalities. (English) Zbl 1219.90172
Summary: In this paper, we use the auxiliary principle technique to suggest and analyze an implicit iterative method for solving bifunction variational inequalities. We also study the convergence criteria of this new method under pseudomonotonicity condition.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
References:
[1]Crespi, G.P.J., Ginchev, J., Rocca, M.: Minty variational inequalities, increase along rays property and optimization. J. Optim. Theory Appl. 123, 479–496 (2004) · Zbl 1059.49010 · doi:10.1007/s10957-004-5719-y
[2]Crespi, G.P.J., Ginchev, J., Rocca, M.: Existence of solutions and star-shapedness in Minty variational inequalities. J. Glob. Optim. 32, 485–494 (2005) · Zbl 1097.49007 · doi:10.1007/s10898-003-2685-0
[3]Crespi, G.P.J., Ginchev, J., Rocca, M.: Increasing along rays property for vector functions. J. Nonconvex Anal. 7, 39–50 (2006)
[4]Crespi, G.P.J., Ginchev, J., Rocca, M.: Some remarks on the Minty vector variational principle. J. Math. Anal. Appl. 345, 165–175 (2008) · Zbl 1152.49007 · doi:10.1016/j.jmaa.2008.03.012
[5]Fang, Y.P., Hu, R.: Parametric well-posedness for variational inequalities defined by bifunction. Comput. Math. Appl. 53, 1306–1316 (2007) · Zbl 1168.49307 · doi:10.1016/j.camwa.2006.09.009
[6]Lalitha, C.S., Mehra, M.: Vector variational inequalities with cone-pseudomonotone bifunction. Optimization 54, 327–338 (2005) · Zbl 1087.90069 · doi:10.1080/02331930500100254
[7]Noor, M.A.: Some new classes of nonconvex functions. Nonlinear Funct. Anal. Appl. 11, 165–171 (2006)
[8]Gloawinski, R., Lions, L.J., Tremolieres, R.: Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam (1981)
[9]Stampacchia, G.: Formes bilineaires coercitives sur les ensembles convexes. C. R. Acad. Sci. Paris 258, 4413–4416 (1964)
[10]Noor, M.A.: New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 251, 217–229 (2000) · Zbl 0964.49007 · doi:10.1006/jmaa.2000.7042
[11]Noor, M.A.: Auxiliary principle technique for equilibrium problems. J. Optim. Theory Appl. 122, 371–386 (2004) · Zbl 1092.49010 · doi:10.1023/B:JOTA.0000042526.24671.b2
[12]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 · doi:10.1016/0377-0427(93)90058-J
[13]Zhu, D.L., Marcotte, P.: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM J. Optim. 6, 714–726 (1996) · Zbl 0855.47043 · doi:10.1137/S1052623494250415
[14]Noor, M.A.: Some developments in general variational inequalities. Appl. Math. Comput. 152, 199–277 (2004) · Zbl 1134.49304 · doi:10.1016/S0096-3003(03)00558-7