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Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces
1. | Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China |
2. | Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064 |
References:
[1] |
M. Adivar and S. C. Fang, Convex optimization on mixed domains,, J. Ind. Manag. Optim., 8 (2012), 189.
|
[2] |
R. P. Agarwal, Y. J. Cho and N. Petrot, Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces,, Fixed Point Theory Appl., 2011 (2011).
|
[3] |
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.
doi: 10.1016/j.jmaa.2004.03.014. |
[4] |
L. C. Ceng, S. Schaible and J. C. Yao, Existence of solutions for generalized vector variational-like inequalities,, J. Optim. Theory Appl., 137 (2008), 121.
doi: 10.1007/s10957-007-9336-4. |
[5] |
Y. F. Chai, Y. J. Cho and J. Li, Some characterizations of ideal point in vector optimization problems,, J. Inequal. Appl., 2008 (2008).
|
[6] |
C. R. Chen, T. C. Edwin Cheng, S. J. Li and X. Q. Yang, Nolinear augmented lagrangian for nonconvex multiobjective optimization,, J. Ind. Manag. Optim., 7 (2011), 157.
doi: 10.3934/jimo.2011.7.157. |
[7] |
C. R. Chen, S. J. Li and Z. M. Fang, On the solution semicontinuity to a parametric generalized vector quasivariational inequality,, Comput. Math. Appl., 60 (2010), 2417.
doi: 10.1016/j.camwa.2010.08.036. |
[8] |
G. Y. Chen, X. X. Huang and X. Q. Yang, "Vector Optimization: Set-Valued and Variational Analysis,", in, 541 (2005).
|
[9] |
G. Y. Chen and S. J. Li, Existence of solutions for a generalized vector quasivariational inequality,, J. Optim. Theory Appl., 90 (1996), 321.
doi: 10.1007/BF02190001. |
[10] |
J. W. Chen, Y. J. Cho, J. K. Kim and J. Li, Multiobjective optimization problems with modified objective functions and cone constraints and applications,, J. Global Optim., 49 (2011), 137.
|
[11] |
Y. H. Cheng and D. L. Zhu, Global stability results for the weak vector variational inequality,, J. Global Optim., 32 (2005), 543.
|
[12] |
Y. Chiang, Semicontinuous mappings into T. V. S. with applications to mixed vector variational-like inequalities,, J. Global Optim., 32 (2005), 467.
doi: 10.1007/s10898-003-2684-1. |
[13] |
Y. J. Cho and N. Petrot, An optimization problem related to generalized equilibrium and fixed point problems with applications,, Fixed Point Theory, 11 (2010), 237.
|
[14] |
S. Deng, Characterizations of the nonemptiness and boundedness of weakly efficient solution sets of convex vector optimization problems in real reflexive Banach spaces,, J. Optim. Theory Appl., 140 (2009), 1.
|
[15] |
F. Giannessi, Theorems of alterative, quadratic programs and complementarity problems,, in, (1980), 151.
|
[16] |
F. Giannessi, "Vector Variational Inequalities and Vector Equilibria: Mathematical Theories,", Kluwer Academic Publishers, (2000).
|
[17] |
Y. R. He, Stable pseudomonotone variational inequality in reflexive Banach space,, J. Math. Anal. Appl., 330 (2007), 352.
|
[18] |
N. J. Huang and Y. P. Fang, On vector variational inequalities in reflexive Banach spaces,, J. Global Optim., 32 (2005), 495.
|
[19] |
P. Q. Khanh and L. M. Luu, Upper semicontinuity of the solution set to parametric vector quasivariational inequalities,, J. Global Optim., 32 (2005), 569.
doi: 10.1007/s10898-004-2694-7. |
[20] |
K. Kimura and J. C. Yao, Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems,, J. Ind. Manag. Optim., 4 (2008), 167.
doi: 10.3934/jimo.2008.4.167. |
[21] |
G. M. Lee and K. B. Lee, Vector variational inequalities for nondifferentiable convex vector optimization problems,, J. Glob. Optim., 32 (2005), 597.
doi: 10.1007/s10898-004-2696-5. |
[22] |
S. J. Li and C. R. Chen, Stability of weak vector variational inequality,, Nonlinear Anal., 70 (2009), 1528.
|
[23] |
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.
doi: 10.1023/A:1014830925232. |
[24] |
S. J. Li and X. L. Guo, Calculus rules of generalized $\varepsilon$-subdifferential for vector valued mappings and applications,, J. Ind. Manag. Optim., 8 (2012), 411.
doi: 10.3934/jimo.2012.8.411. |
[25] |
R. T. Rochafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[26] |
M. Sion, On general minimax theorems,, Pacific J. Math., 8 (1958), 171.
|
[27] |
X. Q. Yang and J. C. Yao, Gap functions and existence of solutions to set-valued vector variational inequalities,, J. Optim. Theory Appl., 115 (2002), 407.
doi: 10.1023/A:1020844423345. |
[28] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem,, J. Ind. Manag. Optim., 8 (2012), 485.
doi: 10.3934/jimo.2012.8.485. |
[29] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, J. Ind. Manag. Optim., 6 (2010), 895.
doi: 10.3934/jimo.2010.6.895. |
[30] |
R. Y. Zhong and N. J. Huang, Stability analysis for minty mixed variational inequality in reflexive Banach spaces,, J. Optim. Theory Appl., 147 (2010), 454.
doi: 10.1007/s10957-010-9732-z. |
[31] |
J. Zhu, Y. J. Zhong and Y. J. Cho, Generalized variational principle and vector optimization,, J. Optim. Theory Appl., 106 (2000), 201.
doi: 10.1023/A:1004619426652. |
show all references
References:
[1] |
M. Adivar and S. C. Fang, Convex optimization on mixed domains,, J. Ind. Manag. Optim., 8 (2012), 189.
|
[2] |
R. P. Agarwal, Y. J. Cho and N. Petrot, Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces,, Fixed Point Theory Appl., 2011 (2011).
|
[3] |
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.
doi: 10.1016/j.jmaa.2004.03.014. |
[4] |
L. C. Ceng, S. Schaible and J. C. Yao, Existence of solutions for generalized vector variational-like inequalities,, J. Optim. Theory Appl., 137 (2008), 121.
doi: 10.1007/s10957-007-9336-4. |
[5] |
Y. F. Chai, Y. J. Cho and J. Li, Some characterizations of ideal point in vector optimization problems,, J. Inequal. Appl., 2008 (2008).
|
[6] |
C. R. Chen, T. C. Edwin Cheng, S. J. Li and X. Q. Yang, Nolinear augmented lagrangian for nonconvex multiobjective optimization,, J. Ind. Manag. Optim., 7 (2011), 157.
doi: 10.3934/jimo.2011.7.157. |
[7] |
C. R. Chen, S. J. Li and Z. M. Fang, On the solution semicontinuity to a parametric generalized vector quasivariational inequality,, Comput. Math. Appl., 60 (2010), 2417.
doi: 10.1016/j.camwa.2010.08.036. |
[8] |
G. Y. Chen, X. X. Huang and X. Q. Yang, "Vector Optimization: Set-Valued and Variational Analysis,", in, 541 (2005).
|
[9] |
G. Y. Chen and S. J. Li, Existence of solutions for a generalized vector quasivariational inequality,, J. Optim. Theory Appl., 90 (1996), 321.
doi: 10.1007/BF02190001. |
[10] |
J. W. Chen, Y. J. Cho, J. K. Kim and J. Li, Multiobjective optimization problems with modified objective functions and cone constraints and applications,, J. Global Optim., 49 (2011), 137.
|
[11] |
Y. H. Cheng and D. L. Zhu, Global stability results for the weak vector variational inequality,, J. Global Optim., 32 (2005), 543.
|
[12] |
Y. Chiang, Semicontinuous mappings into T. V. S. with applications to mixed vector variational-like inequalities,, J. Global Optim., 32 (2005), 467.
doi: 10.1007/s10898-003-2684-1. |
[13] |
Y. J. Cho and N. Petrot, An optimization problem related to generalized equilibrium and fixed point problems with applications,, Fixed Point Theory, 11 (2010), 237.
|
[14] |
S. Deng, Characterizations of the nonemptiness and boundedness of weakly efficient solution sets of convex vector optimization problems in real reflexive Banach spaces,, J. Optim. Theory Appl., 140 (2009), 1.
|
[15] |
F. Giannessi, Theorems of alterative, quadratic programs and complementarity problems,, in, (1980), 151.
|
[16] |
F. Giannessi, "Vector Variational Inequalities and Vector Equilibria: Mathematical Theories,", Kluwer Academic Publishers, (2000).
|
[17] |
Y. R. He, Stable pseudomonotone variational inequality in reflexive Banach space,, J. Math. Anal. Appl., 330 (2007), 352.
|
[18] |
N. J. Huang and Y. P. Fang, On vector variational inequalities in reflexive Banach spaces,, J. Global Optim., 32 (2005), 495.
|
[19] |
P. Q. Khanh and L. M. Luu, Upper semicontinuity of the solution set to parametric vector quasivariational inequalities,, J. Global Optim., 32 (2005), 569.
doi: 10.1007/s10898-004-2694-7. |
[20] |
K. Kimura and J. C. Yao, Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems,, J. Ind. Manag. Optim., 4 (2008), 167.
doi: 10.3934/jimo.2008.4.167. |
[21] |
G. M. Lee and K. B. Lee, Vector variational inequalities for nondifferentiable convex vector optimization problems,, J. Glob. Optim., 32 (2005), 597.
doi: 10.1007/s10898-004-2696-5. |
[22] |
S. J. Li and C. R. Chen, Stability of weak vector variational inequality,, Nonlinear Anal., 70 (2009), 1528.
|
[23] |
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.
doi: 10.1023/A:1014830925232. |
[24] |
S. J. Li and X. L. Guo, Calculus rules of generalized $\varepsilon$-subdifferential for vector valued mappings and applications,, J. Ind. Manag. Optim., 8 (2012), 411.
doi: 10.3934/jimo.2012.8.411. |
[25] |
R. T. Rochafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[26] |
M. Sion, On general minimax theorems,, Pacific J. Math., 8 (1958), 171.
|
[27] |
X. Q. Yang and J. C. Yao, Gap functions and existence of solutions to set-valued vector variational inequalities,, J. Optim. Theory Appl., 115 (2002), 407.
doi: 10.1023/A:1020844423345. |
[28] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem,, J. Ind. Manag. Optim., 8 (2012), 485.
doi: 10.3934/jimo.2012.8.485. |
[29] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, J. Ind. Manag. Optim., 6 (2010), 895.
doi: 10.3934/jimo.2010.6.895. |
[30] |
R. Y. Zhong and N. J. Huang, Stability analysis for minty mixed variational inequality in reflexive Banach spaces,, J. Optim. Theory Appl., 147 (2010), 454.
doi: 10.1007/s10957-010-9732-z. |
[31] |
J. Zhu, Y. J. Zhong and Y. J. Cho, Generalized variational principle and vector optimization,, J. Optim. Theory Appl., 106 (2000), 201.
doi: 10.1023/A:1004619426652. |
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