-
Previous Article
Effective heuristics for makespan minimization in parallel batch machines with non-identical capacities and job release times
- JIMO Home
- This Issue
-
Next Article
An optimal trade-off model for portfolio selection with sensitivity of parameters
Continuity of the solution mappings to parametric generalized non-weak vector Ky Fan inequalities
| a. | College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China |
| b. | College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China |
In this paper, by using the nonlinear scalarization method and under some new assumptions, which do not involve any information on the solution set, we establish the continuity of solution mappings of parametric generalized non-weak vector Ky Fan inequality with moving cones. The results are new and improve corresponding ones in the literature. Some examples are given to illustrate our results.
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,
Continuity of solution maps of parametric quasiequilibrium problems, J. Global Optim., 46 (2010), 247-259.
doi: 10.1007/s10898-009-9422-2. |
| [3] |
J. -P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 2006. |
| [4] |
C. Berge, Topological Spaces, Oliver and Boy1, London, 1963, Dover Publications, Inc., Mineola, NY, 1997. |
| [5] |
B. Chen and N. J. Huang,
Continuity of the solution mapping to parametric generalized vector equilibrium problems, J. Global Optim., 56 (2013), 1515-1528.
doi: 10.1007/s10898-012-9904-5. |
| [6] |
C. R. Chen, S. J. Li and K. L. Teo,
Solution semicontinuity of parametric generalized vector equilibrium problems, J. Global Optim., 45 (2009), 309-318.
doi: 10.1007/s10898-008-9376-9. |
| [7] |
G. Y. Chen, X. Q. Yang and H. Yu,
A nonlinear scalarization function and generalized quasi-vector equilibrium problems, J. Global Optim., 32 (2005), 451-466.
doi: 10.1007/s10898-003-2683-2. |
| [8] |
Y. H. Cheng and D. L. Zhu,
Global stability results for the weak vector variational inequality, J. Global Optim., 32 (2005), 543-550.
doi: 10.1007/s10898-004-2692-9. |
| [9] |
K. Fan,
Extension of two fixed point theorems of F.E., Browder, Math. Z., 112 (1969), 234-240.
doi: 10.1007/BF01110225. |
| [10] |
F. Ferro,
A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60 (1989), 19-31.
doi: 10.1007/BF00938796. |
| [11] |
F. Giannessi, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-1-4613-0299-5. |
| [12] |
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. |
| [13] |
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. |
| [14] |
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. |
| [15] |
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. |
| [16] |
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. |
| [17] |
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. |
| [18] |
S. J. Li, H. M. Liu and C. R. Chen,
Lower semicomtinuity of parametric generalized weak vector equilibrium problems, Bull. Aust. Math. Soc., 81 (2010), 85-95.
doi: 10.1017/S0004972709000628. |
| [19] |
Z. Y. Peng and S. S. Chang,
On the lower semicontinuity of the set of efficient solutions to parametric generalized systems, Optim. Lett., 8 (2014), 159-169.
doi: 10.1007/s11590-012-0544-y. |
| [20] |
Z. Y. Peng, X. M. Yang and J. W. Peng,
On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality, J. Optim. Theory Appl., 152 (2012), 256-264.
doi: 10.1007/s10957-011-9883-6. |
| [21] |
P. H. Sach,
New nonlinear scalarization functions and applications, Nonlinear Anal., 75 (2012), 2281-2292.
doi: 10.1016/j.na.2011.10.028. |
| [22] |
P. H. Sach and N. B. Minh,
Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities, J. Global Optim., 57 (2013), 1401-1418.
doi: 10.1007/s10898-012-0015-0. |
| [23] |
P. H. Sach and L. A. Tuan,
New scalarizing approach to the stability analysis in parametric generalized Ky Fan inequality problems, J. Optim. Theory Appl., 157 (2013), 347-364.
doi: 10.1007/s10957-012-0105-7. |
| [24] |
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. |
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,
Continuity of solution maps of parametric quasiequilibrium problems, J. Global Optim., 46 (2010), 247-259.
doi: 10.1007/s10898-009-9422-2. |
| [3] |
J. -P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 2006. |
| [4] |
C. Berge, Topological Spaces, Oliver and Boy1, London, 1963, Dover Publications, Inc., Mineola, NY, 1997. |
| [5] |
B. Chen and N. J. Huang,
Continuity of the solution mapping to parametric generalized vector equilibrium problems, J. Global Optim., 56 (2013), 1515-1528.
doi: 10.1007/s10898-012-9904-5. |
| [6] |
C. R. Chen, S. J. Li and K. L. Teo,
Solution semicontinuity of parametric generalized vector equilibrium problems, J. Global Optim., 45 (2009), 309-318.
doi: 10.1007/s10898-008-9376-9. |
| [7] |
G. Y. Chen, X. Q. Yang and H. Yu,
A nonlinear scalarization function and generalized quasi-vector equilibrium problems, J. Global Optim., 32 (2005), 451-466.
doi: 10.1007/s10898-003-2683-2. |
| [8] |
Y. H. Cheng and D. L. Zhu,
Global stability results for the weak vector variational inequality, J. Global Optim., 32 (2005), 543-550.
doi: 10.1007/s10898-004-2692-9. |
| [9] |
K. Fan,
Extension of two fixed point theorems of F.E., Browder, Math. Z., 112 (1969), 234-240.
doi: 10.1007/BF01110225. |
| [10] |
F. Ferro,
A minimax theorem for vector-valued functions, J. Optim. Theory Appl., 60 (1989), 19-31.
doi: 10.1007/BF00938796. |
| [11] |
F. Giannessi, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, 2000.
doi: 10.1007/978-1-4613-0299-5. |
| [12] |
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. |
| [13] |
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. |
| [14] |
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. |
| [15] |
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. |
| [16] |
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. |
| [17] |
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. |
| [18] |
S. J. Li, H. M. Liu and C. R. Chen,
Lower semicomtinuity of parametric generalized weak vector equilibrium problems, Bull. Aust. Math. Soc., 81 (2010), 85-95.
doi: 10.1017/S0004972709000628. |
| [19] |
Z. Y. Peng and S. S. Chang,
On the lower semicontinuity of the set of efficient solutions to parametric generalized systems, Optim. Lett., 8 (2014), 159-169.
doi: 10.1007/s11590-012-0544-y. |
| [20] |
Z. Y. Peng, X. M. Yang and J. W. Peng,
On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality, J. Optim. Theory Appl., 152 (2012), 256-264.
doi: 10.1007/s10957-011-9883-6. |
| [21] |
P. H. Sach,
New nonlinear scalarization functions and applications, Nonlinear Anal., 75 (2012), 2281-2292.
doi: 10.1016/j.na.2011.10.028. |
| [22] |
P. H. Sach and N. B. Minh,
Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities, J. Global Optim., 57 (2013), 1401-1418.
doi: 10.1007/s10898-012-0015-0. |
| [23] |
P. H. Sach and L. A. Tuan,
New scalarizing approach to the stability analysis in parametric generalized Ky Fan inequality problems, J. Optim. Theory Appl., 157 (2013), 347-364.
doi: 10.1007/s10957-012-0105-7. |
| [24] |
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. |
| [1] |
Chunrong Chen, Zhimiao Fang. A note on semicontinuity to a parametric generalized Ky Fan inequality. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 779-784. doi: 10.3934/naco.2012.2.779 |
| [2] |
Matheus C. Bortolan, José Manuel Uzal. Upper and weak-lower semicontinuity of pullback attractors to impulsive evolution processes. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3667-3692. doi: 10.3934/dcdsb.2020252 |
| [3] |
Micol Amar, Virginia De Cicco. Lower semicontinuity for polyconvex integrals without coercivity assumptions. Evolution Equations and Control Theory, 2014, 3 (3) : 363-372. doi: 10.3934/eect.2014.3.363 |
| [4] |
Yonghai Wang. On the upper semicontinuity of pullback attractors with applications to plate equations. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1653-1673. doi: 10.3934/cpaa.2010.9.1653 |
| [5] |
Qilin Wang, Shengji Li. Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1225-1234. doi: 10.3934/jimo.2014.10.1225 |
| [6] |
Yonghai Wang, Chengkui Zhong. Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3189-3209. doi: 10.3934/dcds.2013.33.3189 |
| [7] |
Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4899-4912. doi: 10.3934/dcdsb.2019036 |
| [8] |
Ahmed Y. Abdallah. Upper semicontinuity of the attractor for a second order lattice dynamical system. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 899-916. doi: 10.3934/dcdsb.2005.5.899 |
| [9] |
María Astudillo, Marcelo M. Cavalcanti. On the upper semicontinuity of the global attractor for a porous medium type problem with large diffusion. Evolution Equations and Control Theory, 2017, 6 (1) : 1-13. doi: 10.3934/eect.2017001 |
| [10] |
Zaiyun Peng, Xinmin Yang, Kok Lay Teo. On the Hölder continuity of approximate solution mappings to parametric weak generalized Ky Fan Inequality. Journal of Industrial and Management Optimization, 2015, 11 (2) : 549-562. doi: 10.3934/jimo.2015.11.549 |
| [11] |
Linfang Liu, Xianlong Fu. Existence and upper semicontinuity of (L2, Lq) pullback attractors for a stochastic p-laplacian equation. Communications on Pure and Applied Analysis, 2017, 6 (2) : 443-474. doi: 10.3934/cpaa.2017023 |
| [12] |
Shengfan Zhou, Caidi Zhao, Yejuan Wang. Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1259-1277. doi: 10.3934/dcds.2008.21.1259 |
| [13] |
Ling Xu, Jianhua Huang, Qiaozhen Ma. Upper semicontinuity of random attractors for the stochastic non-autonomous suspension bridge equation with memory. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 5959-5979. doi: 10.3934/dcdsb.2019115 |
| [14] |
Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice systems with random coupled coefficients. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2221-2245. doi: 10.3934/cpaa.2016035 |
| [15] |
Yejuan Wang. On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3669-3708. doi: 10.3934/dcdsb.2016116 |
| [16] |
Wenlong Sun. The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay. Electronic Research Archive, 2020, 28 (3) : 1343-1356. doi: 10.3934/era.2020071 |
| [17] |
Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2787-2812. doi: 10.3934/dcds.2017120 |
| [18] |
Na Lei, Shengfan Zhou. Upper semicontinuity of pullback attractors for non-autonomous lattice systems under singular perturbations. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 73-108. doi: 10.3934/dcds.2021108 |
| [19] |
C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a set-valued weak vector variational inequality. Journal of Industrial and Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519 |
| [20] |
Minghua Li, Chunrong Chen, Shengjie Li. Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1261-1272. doi: 10.3934/jimo.2019001 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]