
Previous Article
A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi$f_i$expansive mappings in convex metric spaces
 NACO Home
 This Issue

Next Article
An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors
Existence of solutions and $\alpha$wellposedness for a system of constrained setvalued variational inequalities
1.  School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 
2.  School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 
References:
[1] 
R. T. Agarwal, N. J. Huang and Y. J. Cho, Generalized nonlinear mixed implicit quasivariational inclusions with setvalued mappings,, J. Inequal. Appl., 7 (2002), 807. 
[2] 
H. Attouch, "E.D.P.associées à de sousdifférentiels,", Thèse de Doctorat d'état ES Sciences Mathématiques, (1976). 
[3] 
L. C. Ceng, N. Hadjisavvas, S. Schaible and J. C. Yao, Wellposedness for mixed quasivariationallike inequalities,, J. Optim. Theory Appl., 139 (2008), 109. doi: 10.1007/s1095700894289. 
[4] 
J. W. Chen, Z. Wan and Y. J. Cho, LevitinPolyak wellposedness by perturbations for systems of setvalued vector quasiequilibrium problems,, Math. Meth. Oper. Res., 77 (2013), 33. doi: 10.1007/s0018601204145. 
[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: 10.1186/1029242X201149. 
[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. 
[7] 
Y. P. Fang, R. Hu and N. J. Huang, Wellposedness for equilibrium problems and for optimization problems with equilibrium constraints,, Comput. Math. Appl., 55 (2008), 89. doi: 10.1016/j.camwa.2007.03.019. 
[8] 
M. Furi and A. Vignoli, About wellposed optimization problems for functions in metric spaces,, J. Optim. Theory Appl., 5 (1970), 225. doi: 10.1007/BF00927717. 
[9] 
X. X. Huang and X. Q. Yang, LevitinPolyak wellposedness in generalized variational inequalities problems with functional constraints,, J. Ind. Manag. Optim., 3 (2007), 671. doi: 10.3934/jimo.2007.3.671. 
[10] 
X. X. Huang and X. Q. Yang, LevitinPolyak wellposedness of vector variational inequality problems with functional constraints,, Numer. Funct. Anal. Optim., 31 (2010), 671. doi: 10.1080/01630563.2010.485296. 
[11] 
R. Hu, Y. P. Fang, N. J. Huang and M. M. Wong, Wellposedness of systems of equilibrium problems,, Taiwanese J. Math., 14 (2010), 2435. 
[12] 
R. Hu, Y. P. Fang and N. J. Huang, LevitinPolyak wellposedness for variational inequalities and for optimization problems with variational inequalities,, J. Ind. Manag. Optim., 6 (2010), 465. 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. 
[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. 
[15] 
K. Kuratowski, "Topology,", (Vols. 1 and 2), (1968). 
[16] 
C. S. Lalitha and G. Bhatia, Wellposedness for parametric quasivariational inequality problems and for optimizations problems with quasivariational inequality constraints,, Optim., 59 (2010), 997. doi: 10.1080/02331930902878358. 
[17] 
M. B. Lignola and J. Morgan, Wellposedness for optimization problems with constraints defined by variational inequalities having a unique solution,, J. Glob. Optim., 16 (2000), 57. doi: 10.1023/A:1008370910807. 
[18] 
M. B. Lignola and J. Morgan, Approximating solutions and $\alpha$wellposedness for variational inequalities and Nash equilibria,, in:, (2001), 367. 
[19] 
M. B. Lignola and J. Morgan, αwellposedness for Nash equilibria and for optimization problems with Nash equilibrium constraints,, J. Glob. Optim., 36 (2006), 439. doi: 10.1007/s1089800690205. 
[20] 
P. L. Lions, Two remarks on the convergence of convex functions and monotone operator,, Nonlinear Anal., 2 (1978), 553. 
[21] 
R. Lucchetti and F. Patrone, A characterization of Tykhonov wellposedness for minimimum problems with applications to variational inequalities,, Numer. Funct. Anal. Optim., 3 (1981), 461. 
[22] 
P. E. Mainge, New approach to solving a system of variational inequalities and hierarchical problems,, J. Optim. Theory Appl., 138 (2008), 459. doi: 10.1007/s109570089433z. 
[23] 
A. Moudafi and M. A. Noor, Penalty method for a system of constrained variational inequalities,, Optim. Lett., 6 (2012), 451. doi: 10.1007/s1159001002711. 
[24] 
M. A. Noor and K. I. Noor, Projection algorithms for solving a system of general variational inequalities,, Nonlinear Anal., 70 (2009), 2700. doi: 10.1016/j.na.2008.03.057. 
[25] 
D. Pascali and S. Sburlan, "Nonlinear Mappings of Monotone Type,", Martinus Nijhoff, (1978). 
[26] 
J. W. Peng and S. Y. Wu, The generalized Tykhonov wellposedness for system of vector quasiequilibrium problems,, Optim. Lett., 4 (2010), 501. doi: 10.1007/s1159001001799. 
[27] 
J. W. Peng and J. Tang, αwellposedness for mixed quasivariationallike inequality problems,, Abstr. Appl. Anal., 2011 (2011), 1. 
[28] 
G. Stampacchia, Forms bilineaires coercivities sur les ensembles convexes,, CR Acad. Sci. Paris, 258 (1964), 4413. 
[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. 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. 
[31] 
Y. X. Yuan, Recent advances in numerical methods for nonlinear equations and nonlinear least squares,, Numer. Algebra Control Optim., 1 (2011), 15. 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. doi: 10.3934/naco.2011.1.261. 
show all references
References:
[1] 
R. T. Agarwal, N. J. Huang and Y. J. Cho, Generalized nonlinear mixed implicit quasivariational inclusions with setvalued mappings,, J. Inequal. Appl., 7 (2002), 807. 
[2] 
H. Attouch, "E.D.P.associées à de sousdifférentiels,", Thèse de Doctorat d'état ES Sciences Mathématiques, (1976). 
[3] 
L. C. Ceng, N. Hadjisavvas, S. Schaible and J. C. Yao, Wellposedness for mixed quasivariationallike inequalities,, J. Optim. Theory Appl., 139 (2008), 109. doi: 10.1007/s1095700894289. 
[4] 
J. W. Chen, Z. Wan and Y. J. Cho, LevitinPolyak wellposedness by perturbations for systems of setvalued vector quasiequilibrium problems,, Math. Meth. Oper. Res., 77 (2013), 33. doi: 10.1007/s0018601204145. 
[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: 10.1186/1029242X201149. 
[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. 
[7] 
Y. P. Fang, R. Hu and N. J. Huang, Wellposedness for equilibrium problems and for optimization problems with equilibrium constraints,, Comput. Math. Appl., 55 (2008), 89. doi: 10.1016/j.camwa.2007.03.019. 
[8] 
M. Furi and A. Vignoli, About wellposed optimization problems for functions in metric spaces,, J. Optim. Theory Appl., 5 (1970), 225. doi: 10.1007/BF00927717. 
[9] 
X. X. Huang and X. Q. Yang, LevitinPolyak wellposedness in generalized variational inequalities problems with functional constraints,, J. Ind. Manag. Optim., 3 (2007), 671. doi: 10.3934/jimo.2007.3.671. 
[10] 
X. X. Huang and X. Q. Yang, LevitinPolyak wellposedness of vector variational inequality problems with functional constraints,, Numer. Funct. Anal. Optim., 31 (2010), 671. doi: 10.1080/01630563.2010.485296. 
[11] 
R. Hu, Y. P. Fang, N. J. Huang and M. M. Wong, Wellposedness of systems of equilibrium problems,, Taiwanese J. Math., 14 (2010), 2435. 
[12] 
R. Hu, Y. P. Fang and N. J. Huang, LevitinPolyak wellposedness for variational inequalities and for optimization problems with variational inequalities,, J. Ind. Manag. Optim., 6 (2010), 465. 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. 
[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. 
[15] 
K. Kuratowski, "Topology,", (Vols. 1 and 2), (1968). 
[16] 
C. S. Lalitha and G. Bhatia, Wellposedness for parametric quasivariational inequality problems and for optimizations problems with quasivariational inequality constraints,, Optim., 59 (2010), 997. doi: 10.1080/02331930902878358. 
[17] 
M. B. Lignola and J. Morgan, Wellposedness for optimization problems with constraints defined by variational inequalities having a unique solution,, J. Glob. Optim., 16 (2000), 57. doi: 10.1023/A:1008370910807. 
[18] 
M. B. Lignola and J. Morgan, Approximating solutions and $\alpha$wellposedness for variational inequalities and Nash equilibria,, in:, (2001), 367. 
[19] 
M. B. Lignola and J. Morgan, αwellposedness for Nash equilibria and for optimization problems with Nash equilibrium constraints,, J. Glob. Optim., 36 (2006), 439. doi: 10.1007/s1089800690205. 
[20] 
P. L. Lions, Two remarks on the convergence of convex functions and monotone operator,, Nonlinear Anal., 2 (1978), 553. 
[21] 
R. Lucchetti and F. Patrone, A characterization of Tykhonov wellposedness for minimimum problems with applications to variational inequalities,, Numer. Funct. Anal. Optim., 3 (1981), 461. 
[22] 
P. E. Mainge, New approach to solving a system of variational inequalities and hierarchical problems,, J. Optim. Theory Appl., 138 (2008), 459. doi: 10.1007/s109570089433z. 
[23] 
A. Moudafi and M. A. Noor, Penalty method for a system of constrained variational inequalities,, Optim. Lett., 6 (2012), 451. doi: 10.1007/s1159001002711. 
[24] 
M. A. Noor and K. I. Noor, Projection algorithms for solving a system of general variational inequalities,, Nonlinear Anal., 70 (2009), 2700. doi: 10.1016/j.na.2008.03.057. 
[25] 
D. Pascali and S. Sburlan, "Nonlinear Mappings of Monotone Type,", Martinus Nijhoff, (1978). 
[26] 
J. W. Peng and S. Y. Wu, The generalized Tykhonov wellposedness for system of vector quasiequilibrium problems,, Optim. Lett., 4 (2010), 501. doi: 10.1007/s1159001001799. 
[27] 
J. W. Peng and J. Tang, αwellposedness for mixed quasivariationallike inequality problems,, Abstr. Appl. Anal., 2011 (2011), 1. 
[28] 
G. Stampacchia, Forms bilineaires coercivities sur les ensembles convexes,, CR Acad. Sci. Paris, 258 (1964), 4413. 
[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. 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. 
[31] 
Y. X. Yuan, Recent advances in numerical methods for nonlinear equations and nonlinear least squares,, Numer. Algebra Control Optim., 1 (2011), 15. 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. doi: 10.3934/naco.2011.1.261. 
[1] 
Chao Deng, Xiaohua Yao. Wellposedness and illposedness for the 3D generalized NavierStokes equations in $\dot{F}^{\alpha,r}_{\frac{3}{\alpha1}}$. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 437459. doi: 10.3934/dcds.2014.34.437 
[2] 
C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a setvalued weak vector variational inequality. Journal of Industrial & Management Optimization, 2007, 3 (3) : 519528. doi: 10.3934/jimo.2007.3.519 
[3] 
Xing Wang, NanJing Huang. Stability analysis for setvalued vector mixed variational inequalities in real reflexive Banach spaces. Journal of Industrial & Management Optimization, 2013, 9 (1) : 5774. doi: 10.3934/jimo.2013.9.57 
[4] 
JianWen Peng, XinMin Yang. LevitinPolyak wellposedness of a system of generalized vector variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (3) : 701714. doi: 10.3934/jimo.2015.11.701 
[5] 
Rong Hu, YaPing Fang, NanJing Huang. LevitinPolyak wellposedness for variational inequalities and for optimization problems with variational inequality constraints. Journal of Industrial & Management Optimization, 2010, 6 (3) : 465481. doi: 10.3934/jimo.2010.6.465 
[6] 
Qingbang Zhang, Caozong Cheng, Xuanxuan Li. Generalized minimax theorems for two setvalued mappings. Journal of Industrial & Management Optimization, 2013, 9 (1) : 112. doi: 10.3934/jimo.2013.9.1 
[7] 
X. X. Huang, Xiaoqi Yang. LevitinPolyak wellposedness in generalized variational inequality problems with functional constraints. Journal of Industrial & Management Optimization, 2007, 3 (4) : 671684. doi: 10.3934/jimo.2007.3.671 
[8] 
Shay Kels, Nira Dyn. Bernsteintype approximation of setvalued functions in the symmetric difference metric. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 10411060. doi: 10.3934/dcds.2014.34.1041 
[9] 
Zhichun Zhai. Wellposedness for two types of generalized KellerSegel system of chemotaxis in critical Besov spaces. Communications on Pure & Applied Analysis, 2011, 10 (1) : 287308. doi: 10.3934/cpaa.2011.10.287 
[10] 
Vanessa Barros, Felipe Linares. A remark on the wellposedness of a degenerated Zakharov system. Communications on Pure & Applied Analysis, 2015, 14 (4) : 12591274. doi: 10.3934/cpaa.2015.14.1259 
[11] 
Yiming Ding. Renormalization and $\alpha$limit set for expanding Lorenz maps. Discrete & Continuous Dynamical Systems  A, 2011, 29 (3) : 979999. doi: 10.3934/dcds.2011.29.979 
[12] 
Roger Metzger, Carlos Arnoldo Morales Rojas, Phillipe Thieullen. Topological stability in setvalued dynamics. Discrete & Continuous Dynamical Systems  B, 2017, 22 (5) : 19651975. doi: 10.3934/dcdsb.2017115 
[13] 
Dante CarrascoOlivera, Roger Metzger Alvan, Carlos Arnoldo Morales Rojas. Topological entropy for setvalued maps. Discrete & Continuous Dynamical Systems  B, 2015, 20 (10) : 34613474. doi: 10.3934/dcdsb.2015.20.3461 
[14] 
GengHua Li, ShengJie Li. Unified optimality conditions for setvalued optimizations. Journal of Industrial & Management Optimization, 2019, 15 (3) : 11011116. doi: 10.3934/jimo.2018087 
[15] 
Carlos F. Daganzo. On the variational theory of traffic flow: wellposedness, duality and applications. Networks & Heterogeneous Media, 2006, 1 (4) : 601619. doi: 10.3934/nhm.2006.1.601 
[16] 
Shouming Zhou, Chunlai Mu, Liangchen Wang. Wellposedness, blowup phenomena and global existence for the generalized $b$equation with higherorder nonlinearities and weak dissipation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 843867. doi: 10.3934/dcds.2014.34.843 
[17] 
Zhaohui Huo, Boling Guo. The wellposedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems  A, 2005, 12 (3) : 387402. doi: 10.3934/dcds.2005.12.387 
[18] 
Yongye Zhao, Yongsheng Li, Wei Yan. Local Wellposedness and Persistence Property for the Generalized Novikov Equation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 803820. doi: 10.3934/dcds.2014.34.803 
[19] 
Yu Zhang, Tao Chen. Minimax problems for setvalued mappings with set optimization. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 327340. doi: 10.3934/naco.2014.4.327 
[20] 
Alexander V. Rezounenko, Petr Zagalak. Nonlocal PDEs with discrete statedependent delays: Wellposedness in a metric space. Discrete & Continuous Dynamical Systems  A, 2013, 33 (2) : 819835. doi: 10.3934/dcds.2013.33.819 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]