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)
A new hybrid iterative algorithm for variational inequalities. (English) Zbl 1191.65080
An iterative method is devised for solving variational inequalities with strongly monotone Lipschitzian operators. The convergence of the method is proved and it is applied for a constrained generalized pseudoinverse problem.
MSC:
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
49M25Discrete approximations in calculus of variations
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
References:
[1]Stampacchia, G.: Formes bilineaires coercitives sur LES ensembles convexes, CR acad. Sci. Paris 258, 4413-4416 (1964) · Zbl 0124.06401
[2]Glowinski, R.: Numerical methods for nonlinear variational problems, (1984)
[3]Jaillet, P.; Lamberton, D.; Lapeyre, B.: Variational inequalities and the pricing of American options, Acta appl. Math. 21, 263-289 (1990) · Zbl 0714.90004 · doi:10.1007/BF00047211
[4]Oden, J. T.: Qualitative methods on nonlinear mechanics, (1986) · Zbl 0578.70001
[5]Zeidler, E.: Nonlinear functional analysis and its applications, III: Variational methods and applications, (1985) · Zbl 0583.47051
[6]Noor, M. Aslam: Some developments in general variational inequalities, Appl. math. Comput. 152, 199-277 (2004) · Zbl 1134.49304 · doi:10.1016/S0096-3003(03)00558-7
[7]Yamada, I.: The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, 473-504 (2001) · Zbl 1013.49005
[8]Deutsch, F.; Yamada, I.: Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings, Numer. funct. Anal. optimi. 19, 33-56 (1998) · Zbl 0913.47048 · doi:10.1080/01630569808816813
[9]Lions, P. L.: Approximation de points fixes de contractions, CR acad. Sci. Paris 284, 1357-1359 (1977) · Zbl 0349.47046
[10]Xu, H. K.; Kim, T. H.: Convergence of hybrid steepest-descent methods for variational inequalities, J. optim. Theory appl. 119, 185-201 (2003) · Zbl 1045.49018 · doi:10.1023/B:JOTA.0000005048.79379.b6
[11]Takahashi, W.; Shimoji, K.: Convergence theorems for nonexpansive mappings and feasibility problems, Math. comput. Modell. 32, 1463-1471 (2000) · Zbl 0971.47040 · doi:10.1016/S0895-7177(00)00218-1
[12]Shimoji, K.; Takahashi, W.: Strong convergence to common fixed points of infinite nonexpasnsive mappings and applications, Taiwanese J. Math. 5, 387-404 (2001) · Zbl 0993.47037
[13]Yao, Y.; Liou, Y. C.; Yao, J. C.: Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings, Fixed point theory appl. 2007 (2007) · Zbl 1153.54024 · doi:10.1155/2007/64363
[14]Iusem, A. N.: An iterative algorithm for the variational inequality problem, Comput. appl. Math. 13, 103-114 (1994) · Zbl 0811.65049
[15]Censor, Y.; Iusem, A. N.; Zenios, S. A.: An interior point method with Bregman functions for the variational inequality problem with paramonotone operators, Math. program. 81, 373-400 (1998) · Zbl 0919.90123 · doi:10.1007/BF01580089
[16]Bnouhachem, A.: An additional projection step to he and liao’s method for solving variational inequalities, J. comput. Appl. math. 206, 238-250 (2007) · Zbl 1136.49024 · doi:10.1016/j.cam.2006.07.001
[17]Bnouhachem, A.: A new projection and contraction method for linear variational inequalities, J. math. Anal. appl. 314, 513-525 (2006) · Zbl 1079.49002 · doi:10.1016/j.jmaa.2005.03.095
[18]Bnouhachem, A.: An inexact implicit method for general mixed variational inequalities, J. comput. Appl. math. 200, 377-387 (2007) · Zbl 1115.49027 · doi:10.1016/j.cam.2006.01.005
[19]Censor, Y.; Motova, A.; Segal, A.: Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. math. Anal. appl. 327, 1244-1256 (2007)
[20]Censor, Y.; Segal, A.: Algorithms for the quasiconvex feasibility problem, J. comput. Appl. math. 185, 34-50 (2006) · Zbl 1080.65047 · doi:10.1016/j.cam.2005.01.026
[21]Yao, J. C.: Variational inequalities with generalized monotone operators, Math. oper. Res. 19, 691-705 (1994) · Zbl 0813.49010 · doi:10.1287/moor.19.3.691