Abstract
In this note, the lower semicontinuity of the set of efficient solutions to generalized systems is established by using a new proof method which is different from the one used in Gong (J Optim Theory Appl 138:197–205, 2008). Our result improve his corresponding one.
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References
Anh L.Q., Khanh P.Q.: Semicontinuity of the solution set of parametric multivalued vector quasiquilibrium 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)
Anh L.Q., Khanh P.Q.: Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks I: upper semicontinuities. Set-Valued Anal. 16, 267–279 (2008)
Anh, L.Q., Khanh, P.Q.: Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks II: lower semicontinuities applications. Set-Valued Anal. 16, 943–960 (2008)
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., Teo, K.L.: Solution semicontinuity of parametric generalized vector equilibrium problems. J. Glob. Optim. (2008). doi:10.1007/s10898-008-9376-9
Cheng Y.H., Zhu D.L.: Global stability results for the weak vector variational inequality. J. Glob. Optim. 32, 543–550 (2005)
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)
Gong X.H., Yao J.C.: Connectedness of the set of efficient solution for generalized systems. J. Optim. Theory Appl. 138, 189–196 (2008)
Huang N.J., Li J., Thompson H.B.: Stability for parametric implicit vector equilibrium problems. Math. Comput. Model. 43, 1267–1274 (2006)
Kimura K., Yao J.C.: Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems. J. Glob. Optim. 41, 187–202 (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)
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Xu, S., Li, SJ. A new proof approach to lower semicontinuity for parametric vector equilibrium problems. Optim Lett 3, 453–459 (2009). https://doi.org/10.1007/s11590-009-0124-y
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DOI: https://doi.org/10.1007/s11590-009-0124-y