Citation: |
[1] |
M. Adivar and S. C. Fang, Convex optimization on mixed domains, J. Ind. Manag. Optim., 8 (2012), 189-227. |
[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), pp10. |
[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), 699-711.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), 121-133.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), pp.8. Art. ID 231845. |
[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), 157-174.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), 2417-2425.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 "Lecture Notes in Economics and Mathematical System" 541, Springer, Berlin, 2005. |
[9] |
G. Y. Chen and S. J. Li, Existence of solutions for a generalized vector quasivariational inequality, J. Optim. Theory Appl., 90 (1996), 321-334.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), 137-147. |
[11] |
Y. H. Cheng and D. L. Zhu, Global stability results for the weak vector variational inequality, J. Global Optim., 32 (2005), 543-550. |
[12] |
Y. Chiang, Semicontinuous mappings into T. V. S. with applications to mixed vector variational-like inequalities, J. Global Optim., 32 (2005), 467-484.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), 237-250. |
[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), 1-7. |
[15] |
F. Giannessi, Theorems of alterative, quadratic programs and complementarity problems, in "Variational Inequalities and Complementarity Problems" (eds. R. W. Cottle, F. Giannessi and J. L. Lions), Wiley &Sons, New York, (1980), 151-186. |
[16] |
F. Giannessi, "Vector Variational Inequalities and Vector Equilibria: Mathematical Theories," Kluwer Academic Publishers, Dordrecht, Holland, 2000. |
[17] |
Y. R. He, Stable pseudomonotone variational inequality in reflexive Banach space, J. Math. Anal. Appl., 330 (2007), 352-363. |
[18] |
N. J. Huang and Y. P. Fang, On vector variational inequalities in reflexive Banach spaces, J. Global Optim., 32 (2005), 495-505. |
[19] |
P. Q. Khanh and L. M. Luu, Upper semicontinuity of the solution set to parametric vector quasivariational inequalities, J. Global Optim., 32 (2005), 569-580.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), 167-181.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), 597-612.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), 1528-1535. |
[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), 283-295.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), 411-427.doi: 10.3934/jimo.2012.8.411. |
[25] |
R. T. Rochafellar, "Convex Analysis," Princeton University Press, Princeton, 1970. |
[26] |
M. Sion, On general minimax theorems, Pacific J. Math., 8 (1958), 171-176. |
[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), 407-417.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), 485-491.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), 895-910.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), 454-472.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), 201-217.doi: 10.1023/A:1004619426652. |