Citation: |
[1] |
R. T. Agarwal, N. J. Huang and Y. J. Cho, Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings, J. Inequal. Appl., 7 (2002), 807-828. |
[2] |
H. Attouch, "E.D.P.associées à de sous-différentiels," Thèse de Doctorat d'état ES Sciences Mathématiques, Université Paris 6, 1976. |
[3] |
L. C. Ceng, N. Hadjisavvas, S. Schaible and J. C. Yao, Well-posedness for mixed quasivariational-like inequalities, J. Optim. Theory Appl., 139 (2008), 109-125.doi: 10.1007/s10957-008-9428-9. |
[4] |
J. W. Chen, Z. Wan and Y. J. Cho, Levitin-Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems, Math. Meth. Oper. Res., 77 (2013), 33-64.doi: 10.1007/s00186-012-0414-5. |
[5] |
J. W. Chen and Z. Wan, Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces, J. Inequal. Appl., 49 (2011).doi: 10.1186/1029-242X-2011-49. |
[6] |
Y. J. Cho, Y. P. Fang, N. J. Huang and N. J. Hwang, Algorithms for systems of nonlinear variational inequalities, J. Korean Math. Soc., 41 (2004), 203-210. |
[7] |
Y. P. Fang, R. Hu and N. J. Huang, Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints, Comput. Math. Appl., 55 (2008), 89-100.doi: 10.1016/j.camwa.2007.03.019. |
[8] |
M. Furi and A. Vignoli, About well-posed optimization problems for functions in metric spaces, J. Optim. Theory Appl., 5 (1970), 225-229.doi: 10.1007/BF00927717. |
[9] |
X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness in generalized variational inequalities problems with functional constraints, J. Ind. Manag. Optim., 3 (2007), 671-684.doi: 10.3934/jimo.2007.3.671. |
[10] |
X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness of vector variational inequality problems with functional constraints, Numer. Funct. Anal. Optim., 31 (2010), 671-684.doi: 10.1080/01630563.2010.485296. |
[11] |
R. Hu, Y. P. Fang, N. J. Huang and M. M. Wong, Well-posedness of systems of equilibrium problems, Taiwanese J. Math., 14 (2010), 2435-2446. |
[12] |
R. Hu, Y. P. Fang and N. J. Huang, Levitin-Polyak well-posedness for variational inequalities and for optimization problems with variational inequalities, J. Ind. Manag. Optim., 6 (2010), 465-481.doi: 10.3934/jimo.2010.6.465. |
[13] |
G. Kassay, J. Kolumban and Z. Pales, On Nash stationary points, Publ. Math. Debrecen, 54 (1999), 267-279. |
[14] |
J. K. Kim and D. S. Kim, A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces, J. Convex Anal., 11 (2004), 235-243. |
[15] |
K. Kuratowski, "Topology," (Vols. 1 and 2), Academic Press, New York, 1968. |
[16] |
C. S. Lalitha and G. Bhatia, Well-posedness for parametric quasivariational inequality problems and for optimizations problems with quasivariational inequality constraints, Optim., 59 (2010), 997-1011.doi: 10.1080/02331930902878358. |
[17] |
M. B. Lignola and J. Morgan, Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution, J. Glob. Optim., 16 (2000), 57-67.doi: 10.1023/A:1008370910807. |
[18] |
M. B. Lignola and J. Morgan, Approximating solutions and $\alpha$-well-posedness for variational inequalities and Nash equilibria, in: "Decision and Control in Management Science," Kluwer Academic Publishers, (2001), 367-378. |
[19] |
M. B. Lignola and J. Morgan, α-well-posedness for Nash equilibria and for optimization problems with Nash equilibrium constraints, J. Glob. Optim., 36 (2006), 439-459.doi: 10.1007/s10898-006-9020-5. |
[20] |
P. L. Lions, Two remarks on the convergence of convex functions and monotone operator, Nonlinear Anal., 2 (1978), 553-562. |
[21] |
R. Lucchetti and F. Patrone, A characterization of Tykhonov well-posedness for minimimum problems with applications to variational inequalities, Numer. Funct. Anal. Optim., 3 (1981), 461-476. |
[22] |
P. E. Mainge, New approach to solving a system of variational inequalities and hierarchical problems, J. Optim. Theory Appl., 138 (2008), 459-477.doi: 10.1007/s10957-008-9433-z. |
[23] |
A. Moudafi and M. A. Noor, Penalty method for a system of constrained variational inequalities, Optim. Lett., 6 (2012), 451-458.doi: 10.1007/s11590-010-0271-1. |
[24] |
M. A. Noor and K. I. Noor, Projection algorithms for solving a system of general variational inequalities, Nonlinear Anal., 70 (2009), 2700-2706.doi: 10.1016/j.na.2008.03.057. |
[25] |
D. Pascali and S. Sburlan, "Nonlinear Mappings of Monotone Type," Martinus Nijhoff, The Hague, 1978. |
[26] |
J. W. Peng and S. Y. Wu, The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems, Optim. Lett., 4 (2010), 501-512.doi: 10.1007/s11590-010-0179-9. |
[27] |
J. W. Peng and J. Tang, α-well-posedness for mixed quasi-variational-like inequality problems, Abstr. Appl. Anal., 2011 (2011), 1-17. |
[28] |
G. Stampacchia, Forms bilineaires coercivities sur les ensembles convexes, CR Acad. Sci. Paris, 258 (1964), 4413-4416. |
[29] |
Y. Tang and L. W. Liu, The penalty method for a new system of generalized variational inequalities, Int. J. Math. Math. Sci., 2010 (2010), 1-8.doi: 10.1155/2010/614276. |
[30] |
A. N. Tykhonov, On the stability of the functional optimization problem, USSR J. Comput. Math. Math. Phys., 6 (1966), 631-634. |
[31] |
Y. X. Yuan, Recent advances in numerical methods for nonlinear equations and nonlinear least squares, Numer. Algebra Control Optim., 1 (2011), 15-34.doi: 10.3934/naco.2011.1.15. |
[32] |
R. Y. Zhong and N. J. Huang, Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces, Numer. Algebra Control Optim., 1 (2011), 261-274.doi: 10.3934/naco.2011.1.261. |