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Semicontinuity of approximate solution mappings to generalized vector equilibrium problems
1. | College of Sciences, Chongqing Jiaotong University, Chongqing, 400074 |
2. | College of Mathematics and Statistics, Chongqing University, Chongqing, 401331 |
References:
[1] |
L. Q. Anh and P. Q. Khanh, Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J. Math. Anal. Appl., 294 (2004), 699-711.
doi: 10.1016/j.jmaa.2004.03.014. |
[2] |
L. Q. Anh and P. Q. Khanh, On the stability of the solution sets of general multivalued vector quasiequilibrium problems, J. Optim. Theory Appl., 135 (2007), 271-284.
doi: 10.1007/s10957-007-9250-9. |
[3] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. |
[4] |
B. Chen and N. J. Huang, Continuity of the solution mapping to parametric generalized vector equilibrium problems, J. Glob. Optim., 56 (2013), 1515-1528.
doi: 10.1007/s10898-012-9904-5. |
[5] |
C. R. Chen and S. J. Li, Semicontinuity of the solution set map to a set-valued weak vector variational inequality, J. Ind. Manag. Optim., 3 (2007), 519-528.
doi: 10.3934/jimo.2007.3.519. |
[6] |
C. R. Chen and S. J. Li, On the solution continuity of parametric generalized systems, Pac. J. Optim., 6 (2010), 141-151. |
[7] |
C. R. Chen, S. J. Li and K. L. Teo, Solution semicontinuity of parametric generalized vector equilibrium problems, J. Glob. Optim., 45 (2009), 309-318.
doi: 10.1007/s10898-008-9376-9. |
[8] |
Y. H. Cheng and D. L. Zhu, Global stability results for the weak vector variational inequality, J. Glob. Optim., 32 (2005), 543-550.
doi: 10.1007/s10898-004-2692-9. |
[9] |
C. Chiang, O. Chadli and J. C. Yao, Genralized Vector equilibrium problems with trifunctions, J. Glob. Optim., 30 (2004), 135-154.
doi: 10.1007/s10898-004-8273-0. |
[10] |
J. F. Fu, Generalized Vector quasi-equilibrium problems, Math.Methods Oper.Res., 52 (2000), 57-64.
doi: 10.1007/s001860000058. |
[11] |
J. F. Fu, Vector equilibrium problems, existence theorems and convexity of solution set, J. Glob. Optim., 31 (2005), 109-119.
doi: 10.1007/s10898-004-4274-2. |
[12] |
F. Giannessi, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-1-4613-0299-5. |
[13] |
X. H. Gong, Continuity of the solution set to parametric weak vector equilibrium problems, J. Optim. Theory Appl., 139 (2008), 35-46.
doi: 10.1007/s10957-008-9429-8. |
[14] |
X. H. Gong and J. C. Yao, Lower semicontinuity of the set of efficient solutions for generalized systems, J. Optim. Theory Appl., 138 (2008), 197-205.
doi: 10.1007/s10957-008-9379-1. |
[15] |
Y. Han and X. H. Gong, Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems, Appl. Math. Lett., 28 (2014), 38-41.
doi: 10.1016/j.aml.2013.09.006. |
[16] |
N. J. Huang, J. Li and H. B. Thompson, Stability for parametric implicit vector equilibrium problems, Math. Comput. Model., 43 (2006), 1267-1274.
doi: 10.1016/j.mcm.2005.06.010. |
[17] |
P. Q. Khanh and L. M. Luu, Lower and upper semicontinuity of the solution sets and approximate solution sets to parametric multivalued quasivariational inequalities, J. Optim. Theory Appl., 133 (2007), 329-339.
doi: 10.1007/s10957-007-9190-4. |
[18] |
K. Kimura and J. C. Yao, Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems, J. Ind. Manag. Optim., 4 (2008), 167-181.
doi: 10.3934/jimo.2008.4.167. |
[19] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems, J. Glob. Optim., 41 (2008), 187-202.
doi: 10.1007/s10898-007-9210-9. |
[20] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems, Taiwanese J. Math., 12 (2008), 649-669. |
[21] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric generalized quasivector equilibrium problems, Taiwanese J. Math., 12 (2008), 2233-2268. |
[22] |
S. J. Li, G. Y. Chen and K. L. Teo, On the stability of generalized vector quasivariational inequality problems, J. Optim. Theory Appl., 113 (2002), 283-295.
doi: 10.1023/A:1014830925232. |
[23] |
S. J. Li and C. R. Chen, Stability of weak vector variational inequality, Nonlinear Anal., 70 (2009), 1528-1535.
doi: 10.1016/j.na.2008.02.032. |
[24] |
S. J. Li and Z. M. Fang, Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, J. Optim. Theory Appl., 147 (2010), 507-515.
doi: 10.1007/s10957-010-9736-8. |
[25] |
S. J. Li, H. M. Liu, Y. Zhang and Z. M. Fang, Continuity of solution mappings to parametric generalized strong vector equilibrium problems, J. Glob. Optim., 55 (2013), 597-610.
doi: 10.1007/s10898-012-9985-1. |
[26] |
L. J. Lin, Q. H. Ansari and J. Y. Wu, Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems, J. Optim. Theory Appl., 117 (2003), 121-137.
doi: 10.1023/A:1023656507786. |
[27] |
T. Tanino, Stability and sensitivity analysis in convex vector optimization, SIAM J. Control. Optim., 26 (1988), 521-536.
doi: 10.1137/0326031. |
[28] |
Q. L. Wang and S. J. Li, Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem, J. Ind. Manag. Optim., 10 (2014), 1225-1234.
doi: 10.3934/jimo.2014.10.1225. |
[29] |
R. Wangkeeree, R. Wangkeeree and P. Preechasilp, Continuity of the solution mappings to parametric generalized vector equilibrium problems, Appl. Math. Lett., 29 (2014), 42-45.
doi: 10.1016/j.aml.2013.10.012. |
[30] |
W. Y. Zhang, Z. M. Fang and Y. Zhang, A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems, Appl. Math. Lett., 26 (2013), 469-472.
doi: 10.1016/j.aml.2012.11.010. |
show all references
References:
[1] |
L. Q. Anh and P. Q. Khanh, Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J. Math. Anal. Appl., 294 (2004), 699-711.
doi: 10.1016/j.jmaa.2004.03.014. |
[2] |
L. Q. Anh and P. Q. Khanh, On the stability of the solution sets of general multivalued vector quasiequilibrium problems, J. Optim. Theory Appl., 135 (2007), 271-284.
doi: 10.1007/s10957-007-9250-9. |
[3] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. |
[4] |
B. Chen and N. J. Huang, Continuity of the solution mapping to parametric generalized vector equilibrium problems, J. Glob. Optim., 56 (2013), 1515-1528.
doi: 10.1007/s10898-012-9904-5. |
[5] |
C. R. Chen and S. J. Li, Semicontinuity of the solution set map to a set-valued weak vector variational inequality, J. Ind. Manag. Optim., 3 (2007), 519-528.
doi: 10.3934/jimo.2007.3.519. |
[6] |
C. R. Chen and S. J. Li, On the solution continuity of parametric generalized systems, Pac. J. Optim., 6 (2010), 141-151. |
[7] |
C. R. Chen, S. J. Li and K. L. Teo, Solution semicontinuity of parametric generalized vector equilibrium problems, J. Glob. Optim., 45 (2009), 309-318.
doi: 10.1007/s10898-008-9376-9. |
[8] |
Y. H. Cheng and D. L. Zhu, Global stability results for the weak vector variational inequality, J. Glob. Optim., 32 (2005), 543-550.
doi: 10.1007/s10898-004-2692-9. |
[9] |
C. Chiang, O. Chadli and J. C. Yao, Genralized Vector equilibrium problems with trifunctions, J. Glob. Optim., 30 (2004), 135-154.
doi: 10.1007/s10898-004-8273-0. |
[10] |
J. F. Fu, Generalized Vector quasi-equilibrium problems, Math.Methods Oper.Res., 52 (2000), 57-64.
doi: 10.1007/s001860000058. |
[11] |
J. F. Fu, Vector equilibrium problems, existence theorems and convexity of solution set, J. Glob. Optim., 31 (2005), 109-119.
doi: 10.1007/s10898-004-4274-2. |
[12] |
F. Giannessi, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-1-4613-0299-5. |
[13] |
X. H. Gong, Continuity of the solution set to parametric weak vector equilibrium problems, J. Optim. Theory Appl., 139 (2008), 35-46.
doi: 10.1007/s10957-008-9429-8. |
[14] |
X. H. Gong and J. C. Yao, Lower semicontinuity of the set of efficient solutions for generalized systems, J. Optim. Theory Appl., 138 (2008), 197-205.
doi: 10.1007/s10957-008-9379-1. |
[15] |
Y. Han and X. H. Gong, Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems, Appl. Math. Lett., 28 (2014), 38-41.
doi: 10.1016/j.aml.2013.09.006. |
[16] |
N. J. Huang, J. Li and H. B. Thompson, Stability for parametric implicit vector equilibrium problems, Math. Comput. Model., 43 (2006), 1267-1274.
doi: 10.1016/j.mcm.2005.06.010. |
[17] |
P. Q. Khanh and L. M. Luu, Lower and upper semicontinuity of the solution sets and approximate solution sets to parametric multivalued quasivariational inequalities, J. Optim. Theory Appl., 133 (2007), 329-339.
doi: 10.1007/s10957-007-9190-4. |
[18] |
K. Kimura and J. C. Yao, Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems, J. Ind. Manag. Optim., 4 (2008), 167-181.
doi: 10.3934/jimo.2008.4.167. |
[19] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems, J. Glob. Optim., 41 (2008), 187-202.
doi: 10.1007/s10898-007-9210-9. |
[20] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems, Taiwanese J. Math., 12 (2008), 649-669. |
[21] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric generalized quasivector equilibrium problems, Taiwanese J. Math., 12 (2008), 2233-2268. |
[22] |
S. J. Li, G. Y. Chen and K. L. Teo, On the stability of generalized vector quasivariational inequality problems, J. Optim. Theory Appl., 113 (2002), 283-295.
doi: 10.1023/A:1014830925232. |
[23] |
S. J. Li and C. R. Chen, Stability of weak vector variational inequality, Nonlinear Anal., 70 (2009), 1528-1535.
doi: 10.1016/j.na.2008.02.032. |
[24] |
S. J. Li and Z. M. Fang, Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, J. Optim. Theory Appl., 147 (2010), 507-515.
doi: 10.1007/s10957-010-9736-8. |
[25] |
S. J. Li, H. M. Liu, Y. Zhang and Z. M. Fang, Continuity of solution mappings to parametric generalized strong vector equilibrium problems, J. Glob. Optim., 55 (2013), 597-610.
doi: 10.1007/s10898-012-9985-1. |
[26] |
L. J. Lin, Q. H. Ansari and J. Y. Wu, Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems, J. Optim. Theory Appl., 117 (2003), 121-137.
doi: 10.1023/A:1023656507786. |
[27] |
T. Tanino, Stability and sensitivity analysis in convex vector optimization, SIAM J. Control. Optim., 26 (1988), 521-536.
doi: 10.1137/0326031. |
[28] |
Q. L. Wang and S. J. Li, Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem, J. Ind. Manag. Optim., 10 (2014), 1225-1234.
doi: 10.3934/jimo.2014.10.1225. |
[29] |
R. Wangkeeree, R. Wangkeeree and P. Preechasilp, Continuity of the solution mappings to parametric generalized vector equilibrium problems, Appl. Math. Lett., 29 (2014), 42-45.
doi: 10.1016/j.aml.2013.10.012. |
[30] |
W. Y. Zhang, Z. M. Fang and Y. Zhang, A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems, Appl. Math. Lett., 26 (2013), 469-472.
doi: 10.1016/j.aml.2012.11.010. |
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