zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Continuity of the solution set to parametric weak vector equilibrium problems. (English) Zbl 1189.90195
Summary: We obtain some stability results for parametric weak vector equilibrium problems in topological vector spaces. We provide sufficient conditions for the continuity of the solution set mapping in parametric weak monotone vector equilibrium problems.

90C48Programming in abstract spaces
90C31Sensitivity, stability, parametric optimization
[1]Ansari, Q.H., Oettli, W., Schläger, D.: A generalization of vector equilibria. Math. Methods Oper. Res. 46, 147–152 (1997) · Zbl 0889.90155 · doi:10.1007/BF01217687
[2]Bianchi, M., Hadjisavvas, N., Schaible, S.: Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92, 527–542 (1997) · Zbl 0878.49007 · doi:10.1023/A:1022603406244
[3]Giannessi, F.: Theorem of the alternative, quadratic programs, and complementarity problems. In: Cottle, R.W., Giannessi, F., Lions, J.L. (eds.) Variational Inequalities and Complementarity Problems, pp. 151–186. Wiley, New York (1980)
[4]Chen, G.Y.: Existence of solution for a vector variational inequality: an extension of the Hartman-Stampacchia theorem. J. Optim. Theory Appl. 74, 445–456 (1992) · Zbl 0795.49010 · doi:10.1007/BF00940320
[5]Yang, X.Q.: Vector variational inequality and its duality. Nonlinear Anal. Theory Methods Appl. 21, 869–877 (1993) · Zbl 0809.49009 · doi:10.1016/0362-546X(93)90052-T
[6]Yu, S.J., Yao, J.C.: On vector variational inequalities. J. Optim. Theory Appl. 89, 749–769 (1996) · Zbl 0848.49012 · doi:10.1007/BF02275358
[7]Lee, G.M., Lee, B.S., Chang, S.S.: On vector quasivariational inequalities. J. Math. Anal. Appl. 203, 626–638 (1996) · Zbl 0866.49016 · doi:10.1006/jmaa.1996.0401
[8]Konnov, I.V., Yao, J.C.: On the generalized vector variational inequality problem. J. Math. Anal. Appl. 206, 42–58 (1997) · Zbl 0878.49006 · doi:10.1006/jmaa.1997.5192
[9]Fu, J.Y.: Generalized vector quasi-equilibrium problems. Math. Methods Oper. Res. 52, 57–64 (2000) · Zbl 1054.90068 · doi:10.1007/s001860000058
[10]Song, W.: Vector equilibrium problems with set-valued mapping. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, pp. 403–418. Kluwer, Dordrecht (2000)
[11]Lin, L.J., Ansari, Q.H., Wu, J.Y.: Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems. J. Optim. Theory Appl. 117, 121–137 (2003) · Zbl 1063.90062 · doi:10.1023/A:1023656507786
[12]Chiang, C., Chadli, O., Yao, J.C.: Generalized vector equilibrium problems with trifunctions. J. Glob. Optim. 30, 135–154 (2004) · Zbl 1066.90112 · doi:10.1007/s10898-004-8273-0
[13]Ding, X.P., Park, J.Y.: Generalized vector equilibrium problems in generalized convex spaces. J. Optim. Theory Appl. 120, 327–353 (2004) · Zbl 1100.90054 · doi:10.1023/B:JOTA.0000015687.95813.a0
[14]Huang, N.J.: On vector variational inequalities in reflexive Banach spaces. J. Glob. Optim. 32, 495–505 (2005) · Zbl 1097.49009 · doi:10.1007/s10898-003-2686-z
[15]Li, S.J., Chen, G.Y., Teo, K.L.: On the stability of generalized vector quasivariational inequality problems. J. Optim. Theory Appl. 113, 283–295 (2002) · Zbl 1003.47049 · doi:10.1023/A:1014830925232
[16]Cheng, Y.H., Zhu, D.L.: Global stability results for the weak vector variational inequality. J. Glob. Optim. 32, 543–550 (2005) · Zbl 1097.49006 · doi:10.1007/s10898-004-2692-9
[17]Khanh, P.Q., Luu, L.M.: Upper semicontinuity of the solution set to parametric vector quasivariational inequalities. J. Glob. Optim. 32, 569–580 (2005) · Zbl 1097.49013 · doi:10.1007/s10898-004-2694-7
[18]Anh, L.Q., Khanh, P.Q.: Semicontinuity of the solution sets to parametric quasiequilibrium problems. J. Math. Anal. Appl. 294, 699–711 (2004) · Zbl 1048.49004 · doi:10.1016/j.jmaa.2004.03.014
[19]Anh, L.Q., Khanh, P.Q.: On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems. J. Math. Anal. Appl. 321, 308–315 (2006) · Zbl 1104.90041 · doi:10.1016/j.jmaa.2005.08.018
[20]Anh, L.Q., Khanh, P.Q.: On the stability of the solution sets of general multivalued vector quasiequilibrium problems. J. Optim. Theory Appl. 14 (2007). Available online
[21]Anh, L.Q., Khanh, P.Q.: Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces. J. Glob. Optim. 37, 449–465 (2007) · Zbl 1156.90025 · doi:10.1007/s10898-006-9062-8
[22]Bianchi, M., Pini, R.: Sensitivity for parametric vector equilibria. Optimization 55, 221–230 (2006) · Zbl 1149.90156 · doi:10.1080/02331930600662732
[23]Huang, N.J., Li, J., Thompson, H.B.: Stability for parametric implicit vector equilibrium problems. Math. Comput. Model. 43, 1267–1274 (2006) · Zbl 1187.90286 · doi:10.1016/j.mcm.2005.06.010
[24]Ait Mansour, M., Riahi, H.: Sensitivity analysis for abstract equilibrium problems. J. Math. Anal. Appl. 306, 648–691 (2005)
[25]Bianchi, M., Pini, R.: A note on stability for parametric equilibrium problems. Oper. Res. Lett. 31, 445–450 (2003) · Zbl 1112.90082 · doi:10.1016/S0167-6377(03)00051-8
[26]Khanh, P.Q., Luu, L.M.: Lower semicontinuity and upper semicontinuity of the solution sets to parametric multivalued quasivariational inequalities. J. Optim. Theory Appl. 133, 329–339 (2007) · Zbl 1146.49006 · doi:10.1007/s10957-007-9190-4
[27]Gong, X.H.: Efficiency and Henig efficiency for vector equilibrium problems. J. Optim. Theory Appl. 108, 139–154 (2001) · Zbl 1033.90119 · doi:10.1023/A:1026418122905
[28]Gong, X.H.: Connectedness of the solution sets and scalarization for vector equilibrium problems. J. Optim. Theory Appl. 133, 151–161 (2007) · Zbl 1155.90018 · doi:10.1007/s10957-007-9196-y
[29]Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, New York (1985)
[30]Aubin, J.P., Ekeland, I.: Applied Nonlinear Analysis. Wiley, New York (1984)
[31]Muselli, E.: Upper and lower semicontinuity for set-valued mappings involving constraints. J. Optim. Theory Appl. 106, 527–550 (2000) · Zbl 0970.90094 · doi:10.1023/A:1004653312019