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Optimality conditions for vector equilibrium problems and their applications
1. | Technical University of Cluj-Napoca, Department of Mathematics, Str. G. Bariţiu 25, 400027, Cluj-Napoca, Romania |
References:
[1] |
L. Q. Anh, P. Q. Khanh, D. T. M. Van and J. C. Yao, Well-posedness for vector quasiequilibria,, Taiwanese J. Math., 13 (2009), 713.
|
[2] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, On generalized vector equilibrium problems,, Nonlinear Anal., 47 (2001), 543.
doi: 10.1016/S0362-546X(01)00199-7. |
[3] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, Existence of a solution and variational principles for vector equilibrium problems,, J. Optim. Theory Appl., 110 (2001), 481.
doi: 10.1023/A:1017581009670. |
[4] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, Characterizations of solutions for vector equilibrium problems,, J. Optim. Theory Appl., 113 (2002), 435.
doi: 10.1023/A:1015366419163. |
[5] |
Q. H. Ansari, W. Oettli and D. Schläger, A generalization of vectorial equilibria,, Math. Meth. Oper. Res., 46 (1997), 147.
doi: 10.1007/BF01217687. |
[6] |
Q. H. Ansari, X. Q. Yang and J. C. Yao, Existence and duality of implicit vector variational problems,, Numer. Funct. Anal. Optim., 22 (2001), 815.
doi: 10.1081/NFA-100108310. |
[7] |
M. Bianchi, N. Hadjisavvas and S. Schaible, Vector equilibrium problems with generalized monotone bifunctions,, J. Optim. Theory Appl., 92 (1997), 527.
doi: 10.1023/A:1022603406244. |
[8] |
M. Bianchi, G. Kassay and R. Pini, Ekeland's principle for vector equilibrium problems,, Nonlinear Anal., 66 (2007), 1454.
doi: 10.1016/j.na.2006.02.003. |
[9] |
M. Bianchi, G. Kassay and R. Pini, Well-posedness for vector equilibrium problems,, Math. Meth. Oper. Res., 70 (2009), 171.
doi: 10.1007/s00186-008-0239-4. |
[10] |
G. Bigi, A. Capătă and G. Kassay, Existence results for strong vector equilibrium problems and their applications,, Optimization, 61 (2012), 567.
doi: 10.1080/02331934.2010.528761. |
[11] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems,, Math. Stud., 63 (1994), 123.
|
[12] |
J. M. Borwein and R. Goebel, Notions of relative interior in Banach spaces,, J. Math. Sci., 115 (2003), 2542.
doi: 10.1023/A:1022988116044. |
[13] |
J. M. Borwein and A. S. Lewis, Partially finite convex programming, part I: Quasi relative interiors and duality theory,, Math. Prog., 57 (1992), 15.
doi: 10.1007/BF01581072. |
[14] |
J. M. Borwein and V. Jeyakumar, On convexlike Lagrangian and minimax theorems,, Research Report 24, (1988). Google Scholar |
[15] |
F. Cammaroto and B. Di Bella, Separation theorem based on the quasirelative interior and application to duality theory,, J. Optim. Theory Appl., 125 (2005), 223.
doi: 10.1007/s10957-004-1724-4. |
[16] |
A. Capătă and G. Kassay, On vector equilibrium problems and applications,, Taiwanese J. Math., 15 (2011), 365.
|
[17] |
A. Capătă, Optimality conditions for extended Ky Fan inequality with cone and affine constraints and their applications,, J. Optim. Theory. Appl., 152 (2012), 661.
doi: 10.1007/s10957-011-9916-1. |
[18] |
P. Daniele, S. Giuffrè and A. Maugeri, Infinite dimensional duality and applications,, Math. Ann., 339 (2007), 221.
doi: 10.1007/s00208-007-0118-y. |
[19] |
K. Fan, Minimax theorems,, Proc. National Acad. Sci. USA, 39 (1953), 42.
doi: 10.1073/pnas.39.1.42. |
[20] |
K. Fan, A minimax inequality and applications,, in, (1972), 103.
|
[21] |
F. Giannessi, "Vector Variational Inequalities and Vector Equilibria,", Kluwer Academic Publishers, (2000).
doi: 10.1007/978-1-4613-0299-5. |
[22] |
X. H. Gong, Optimality conditions for vector equilibrium problems,, J. Math. Anal. Appl., 342 (2008), 1455.
doi: 10.1016/j.jmaa.2008.01.026. |
[23] |
R. B. Holmes, "Geometric Functional Analysis and its Applications,", Springer-Verlag, (1975).
|
[24] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems,, Taiwanese J. Math., 12 (2008), 649.
|
[25] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric generalized quasi vector equilibrium problems,, Taiwanese J. Math., 12 (2008), 2233.
|
[26] |
M. A. Limber and R. K. Goodrich, Quasi interiors, Lagrange multipliers and $L^p$ spectral estimation with lattice bounds,, J. Optim. Theory Appl., 78 (1993), 143.
doi: 10.1007/BF00940705. |
[27] |
B. C. Ma and X. H. Gong, Optimality conditions for vector equilibrium problems in normed spaces,, Optimization, 60 (2011), 1441.
doi: 10.1080/02331931003657709. |
[28] |
Q. Qiu, Optimality conditions of globally efficient solutions for vector equilibrium problems with generalized convexity,, J. Ineq. Appl., (2009).
doi: 10.1155/2009/898213. |
[29] |
Q. S. Qiu, Optimality conditions for vector equilibrium problems with constraints,, J. Ind. Manag. Optim., 5 (2009), 783.
doi: 10.3934/jimo.2009.5.783. |
[30] |
R. T. Rockafellar, "Conjugate Duality and Optimization,", Society for Industrial and Applied Mathematics, (1974).
|
[31] |
J. Salamon, Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems,, J. Global Optim., 47 (2010), 173.
doi: 10.1007/s10898-009-9464-5. |
[32] |
C. Zălinescu, "Convex Analysis in General Vector Spaces,", World Scientific, (2002).
doi: 10.1142/9789812777096. |
show all references
References:
[1] |
L. Q. Anh, P. Q. Khanh, D. T. M. Van and J. C. Yao, Well-posedness for vector quasiequilibria,, Taiwanese J. Math., 13 (2009), 713.
|
[2] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, On generalized vector equilibrium problems,, Nonlinear Anal., 47 (2001), 543.
doi: 10.1016/S0362-546X(01)00199-7. |
[3] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, Existence of a solution and variational principles for vector equilibrium problems,, J. Optim. Theory Appl., 110 (2001), 481.
doi: 10.1023/A:1017581009670. |
[4] |
Q. H. Ansari, I. V. Konnov and J. C. Yao, Characterizations of solutions for vector equilibrium problems,, J. Optim. Theory Appl., 113 (2002), 435.
doi: 10.1023/A:1015366419163. |
[5] |
Q. H. Ansari, W. Oettli and D. Schläger, A generalization of vectorial equilibria,, Math. Meth. Oper. Res., 46 (1997), 147.
doi: 10.1007/BF01217687. |
[6] |
Q. H. Ansari, X. Q. Yang and J. C. Yao, Existence and duality of implicit vector variational problems,, Numer. Funct. Anal. Optim., 22 (2001), 815.
doi: 10.1081/NFA-100108310. |
[7] |
M. Bianchi, N. Hadjisavvas and S. Schaible, Vector equilibrium problems with generalized monotone bifunctions,, J. Optim. Theory Appl., 92 (1997), 527.
doi: 10.1023/A:1022603406244. |
[8] |
M. Bianchi, G. Kassay and R. Pini, Ekeland's principle for vector equilibrium problems,, Nonlinear Anal., 66 (2007), 1454.
doi: 10.1016/j.na.2006.02.003. |
[9] |
M. Bianchi, G. Kassay and R. Pini, Well-posedness for vector equilibrium problems,, Math. Meth. Oper. Res., 70 (2009), 171.
doi: 10.1007/s00186-008-0239-4. |
[10] |
G. Bigi, A. Capătă and G. Kassay, Existence results for strong vector equilibrium problems and their applications,, Optimization, 61 (2012), 567.
doi: 10.1080/02331934.2010.528761. |
[11] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems,, Math. Stud., 63 (1994), 123.
|
[12] |
J. M. Borwein and R. Goebel, Notions of relative interior in Banach spaces,, J. Math. Sci., 115 (2003), 2542.
doi: 10.1023/A:1022988116044. |
[13] |
J. M. Borwein and A. S. Lewis, Partially finite convex programming, part I: Quasi relative interiors and duality theory,, Math. Prog., 57 (1992), 15.
doi: 10.1007/BF01581072. |
[14] |
J. M. Borwein and V. Jeyakumar, On convexlike Lagrangian and minimax theorems,, Research Report 24, (1988). Google Scholar |
[15] |
F. Cammaroto and B. Di Bella, Separation theorem based on the quasirelative interior and application to duality theory,, J. Optim. Theory Appl., 125 (2005), 223.
doi: 10.1007/s10957-004-1724-4. |
[16] |
A. Capătă and G. Kassay, On vector equilibrium problems and applications,, Taiwanese J. Math., 15 (2011), 365.
|
[17] |
A. Capătă, Optimality conditions for extended Ky Fan inequality with cone and affine constraints and their applications,, J. Optim. Theory. Appl., 152 (2012), 661.
doi: 10.1007/s10957-011-9916-1. |
[18] |
P. Daniele, S. Giuffrè and A. Maugeri, Infinite dimensional duality and applications,, Math. Ann., 339 (2007), 221.
doi: 10.1007/s00208-007-0118-y. |
[19] |
K. Fan, Minimax theorems,, Proc. National Acad. Sci. USA, 39 (1953), 42.
doi: 10.1073/pnas.39.1.42. |
[20] |
K. Fan, A minimax inequality and applications,, in, (1972), 103.
|
[21] |
F. Giannessi, "Vector Variational Inequalities and Vector Equilibria,", Kluwer Academic Publishers, (2000).
doi: 10.1007/978-1-4613-0299-5. |
[22] |
X. H. Gong, Optimality conditions for vector equilibrium problems,, J. Math. Anal. Appl., 342 (2008), 1455.
doi: 10.1016/j.jmaa.2008.01.026. |
[23] |
R. B. Holmes, "Geometric Functional Analysis and its Applications,", Springer-Verlag, (1975).
|
[24] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems,, Taiwanese J. Math., 12 (2008), 649.
|
[25] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric generalized quasi vector equilibrium problems,, Taiwanese J. Math., 12 (2008), 2233.
|
[26] |
M. A. Limber and R. K. Goodrich, Quasi interiors, Lagrange multipliers and $L^p$ spectral estimation with lattice bounds,, J. Optim. Theory Appl., 78 (1993), 143.
doi: 10.1007/BF00940705. |
[27] |
B. C. Ma and X. H. Gong, Optimality conditions for vector equilibrium problems in normed spaces,, Optimization, 60 (2011), 1441.
doi: 10.1080/02331931003657709. |
[28] |
Q. Qiu, Optimality conditions of globally efficient solutions for vector equilibrium problems with generalized convexity,, J. Ineq. Appl., (2009).
doi: 10.1155/2009/898213. |
[29] |
Q. S. Qiu, Optimality conditions for vector equilibrium problems with constraints,, J. Ind. Manag. Optim., 5 (2009), 783.
doi: 10.3934/jimo.2009.5.783. |
[30] |
R. T. Rockafellar, "Conjugate Duality and Optimization,", Society for Industrial and Applied Mathematics, (1974).
|
[31] |
J. Salamon, Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems,, J. Global Optim., 47 (2010), 173.
doi: 10.1007/s10898-009-9464-5. |
[32] |
C. Zălinescu, "Convex Analysis in General Vector Spaces,", World Scientific, (2002).
doi: 10.1142/9789812777096. |
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