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)
Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems. (English) Zbl 1124.49006
Summary: In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result, we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints.
MSC:
49J40Variational methods including variational inequalities
49J53Set-valued and variational analysis
References:
[1]Adly S. (1996) Perturbed algorithm and senstivity analysis for a generalized class of variational J. Math. Anal. 201, 609–630 · Zbl 0856.65077 · doi:10.1006/jmaa.1996.0277
[2]Ahmad R., Ansari Q.H. (2000) An iterative for generalized nonlinear variational inclusion. Appl. Math. Lett. 13(5): 23–26 · Zbl 0954.49006 · doi:10.1016/S0893-9659(00)00028-8
[3]Ahmad R., Ansari Q.H., Irfan S.S. (2005) Generalized variational inclusions and generalized resolvent equations in Banach spaces. Comput. Math. Appl. 49, 1825–1835 · Zbl 1081.49004 · doi:10.1016/j.camwa.2004.10.044
[4]Ansari Q.H., Lin L.J., Su L.B. (2005) Systems of simultaneous generalized vector quasiequilibrium problems and applications. J. Optim. Theory Appl. 127, 27–44 · Zbl 1211.49004 · doi:10.1007/s10957-005-6391-6
[5]Aubin J.P., Cellina A. (1994) Differential Inclusion. Springer Verlag, Berlin, Germany
[6]Bard J.F. (1998) Pratical Bilevel Optimization, Algorithms and Applications, Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrechlt
[7]Birbil S., Bouza G., Frenk J.B.G., Still G. (2006) Equilibrium constrained optimization problems. Eur. J. Operat. Res. 169, 1108–1127 · Zbl 1079.90152 · doi:10.1016/j.ejor.2004.07.075
[8]Blum E., Oettli W. (1994) From optimilization and variational inequalities to equilibrium problems. Math. Students 63, 123–146
[9]Chang S.S. (2000) Set-valued variational inclusion in Banach spaces. J. Math. Anal. Appl. 248, 438–454 · Zbl 1031.49018 · doi:10.1006/jmaa.2000.6919
[10]Ding X.P. (1997) Perturbed proximal point algorithm for generalized quasivariational inclusions. J. Math. Anal. Appl. 210, 88–101 · Zbl 0902.49010 · doi:10.1006/jmaa.1997.5370
[11]Fan K. (1961) A generalization of Tychonoff’s fixed point theorem. Math. Ann. 142, 305–310 · Zbl 0093.36701 · doi:10.1007/BF01353421
[12]Fan K. (1952) Fixed point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38, 121–126 · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121
[13]Fukushima M., Pang J.S. (1998) Some feasible issues in mathematical programs with equilibrium SIMA J. Optim. 8, 673–681
[14]Hassouni A., Moudafi A. (1994) A peturbed algorithm for variational inclusions. J. Math. Anal. Appl. 185, 705–712 · Zbl 0809.49008 · doi:10.1006/jmaa.1994.1277
[15]Himmelberg C.J. (1972) Fixed point of compact multifunctions. J. Math. Anal. Appl. 38, 205–207 · Zbl 0225.54049 · doi:10.1016/0022-247X(72)90128-X
[16]Huang N.J. (1998) Mann and Isbikawa type perturbed iteration algorithm for nonlinear generalized variational inclusions. Comput. Math. Appl. 35(10): 1–7 · Zbl 0999.47057 · doi:10.1016/S0898-1221(98)00066-2
[17]Lin L.J. (2005) Existence theorems of simultaneous equilibrium problems and generalized quasi-saddle points. J. Global Optim. 32, 603–632
[18]Lin L.J. (2005) Existence results for primal and dual generalized vector equilibrium problems with applications to generalized semi-infinite programming. J. Global Optim. 32, 579–597 · Zbl 1097.90069 · doi:10.1007/s10898-004-6096-7
[19]Lin, L.J.: Mathematical program with system of equilibrium constraint. J. Global Optim. (to appear)
[20]Lin L.J. (2006) System of generalized vector quasi-equilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings. J. Global Optim. 34, 15–32 · Zbl 1098.90086 · doi:10.1007/s10898-005-4702-y
[21]Lin, L.J., Hsu, H.W.: Existence theorems of vector quasi-equilibrium problems and mathematical programs with equilibrium constraints. J. Global Optim. (to appear)
[22]Lin, L.J., Huang, Y.J.: Generalized vector quasi-equilibrium problems with applications to fixed point theorems and optimization problems. Nonlinear Anal. (2006) (to appear).
[23]Lin, L.J., Liu, Y.H.: Existence theorems of systems of generalized vector quasi-equilibrium J. Optim. Theory Appl. 130(3), (2006)
[24]Lin L.J., Still G. (2006) Mathematical programs with equilibrium constraints: the existence of feasible points. Optimization 55, 205–219 · Zbl 1124.90033 · doi:10.1080/02331930600703635
[25]Lin L.J., Yu Z.T. (2001) On some equilibrium problems for multimaps. J. Comput. Appl. Math. 129, 171–183 · Zbl 0990.49003 · doi:10.1016/S0377-0427(00)00548-3
[26]Luc D.T. (1989) Theory of Vector Optimization Lectures. Notes in Economics and Mathematical Systems, vol. 319. Springer Verlag, Berlin, Germany
[27]Luo Z.Q., Pang J.S., Ralph D. (1997) Mathematical Program with Equilibrium Constraint. Cambridge University Press, Cambridge
[28]Mordukhovich B.S. (2004) Equilibrium problems with equilibrium constraints via multiobjective optimization. Optim. Methods Soft 19, 479–492 · Zbl 1168.90624 · doi:10.1080/1055678042000218966
[29]Mordukhovich B.S. (2005) Variational Analysis and Generalized Differentiation, vol. I,II. Springer, Herlin, Heidelberg, New York
[30]Robinson S.M. (1979) Generalized equation and their solutions, part I: basic theory. Math Program. Study 10, 128–141
[31]Tan N.X. (1985) Quasi-variational inequalities in topological linear locally convex Hausdorff spaces. Math. Nachrichten 122, 231–245 · doi:10.1002/mana.19851220123