Abstract
In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.
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Anh L.Q., Khanh P.Q.: Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems. J. Math. Anal. Appl. 294, 699–711 (2004)
Anh L.Q., Khanh P.Q.: On the stability of the solution sets of general multivalued vector quasiequilibrium problems. J. Optim. Theory Appl. 135, 271–284 (2007)
Aubin J.P., Ekeland I.: Applied Nonlinear Analysis. Wiley, New York (1984)
Berge C.: Topological Spaces. Oliver and Boyd, London (1963)
Chen C.R., Li S.J.: Semicontinuity of the solution set map to a set-valued weak vector variational inequality. J. Ind. Manag. Optim. 3, 519–528 (2007)
Chen, C.R., Li, S.J.: On the solution continuity of parametric generalized systems. (2008) (submitted)
Chen G.Y., Huang X.X., Yang X.Q.: Vector Optimization: Set-Valued and Variational Analysis. Springer, Berlin (2005)
Chen, C.R., Fang, Z.M., Li, S.J.: On the semicontinuity for a parametric generalized vector quasivariational inequality. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms. (2008) (to appear)
Cheng Y.H., Zhu D.L.: Global stability results for the weak vector variational inequality. J. Global Optim. 32, 543–550 (2005)
Ferro F.: A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 60, 19–31 (1989)
Giannessi, F. (ed.): Vector Variational Inequalities and Vector Equilibria: Mathematical Theories. Kluwer Academic Publishers, Dordrecht (2000)
Gong X.H.: Continuity of the solution set to parametric weak vector equilibrium problems. J. Optim. Theory Appl. 139, 35–46 (2008)
Gong X.H., Yao J.C.: Lower semicontinuity of the set of efficient solutions for generalized systems. J. Optim. Theory Appl. 138, 197–205 (2008)
Huang N.J., Li J., Thompson H.B.: Stability for parametric implicit vector equilibrium problems. Math. Comput. Model. 43, 1267–1274 (2006)
Jahn J.: Vector Optimization-Theory, Applications and Extensions. Springer, Berlin (2004)
Khanh P.Q., Luu L.M.: Upper semicontinuity of the solution set to parametric vector quasivariational inequalities. J. Global Optim. 32, 569–580 (2005)
Kimura K., Yao J.C.: Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems. J. Global Optim. 41, 187–202 (2008)
Kimura K., Yao J.C.: Semicontinuity of solution mappings of parametric generalized vector equilibrium problems. J. Optim. Theory Appl. 138, 429–443 (2008)
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)
Li, S.J., Chen, C.R.: Stability of weak vector variational inequality. Nonlinear Anal. doi:10.1016/j.na.2008.02.032 (2008)
Li S.J., Fang Z.M.: On the stability of a dual weak vector variational inequality problem. J. Ind. Manag. Optim. 4, 155–165 (2008)
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This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073) and the Natural Science Foundation Project of CQ CSTC (Grant number: 2007BB6117).
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Chen, C.R., Li, S.J. & Teo, K.L. Solution semicontinuity of parametric generalized vector equilibrium problems. J Glob Optim 45, 309–318 (2009). https://doi.org/10.1007/s10898-008-9376-9
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DOI: https://doi.org/10.1007/s10898-008-9376-9