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Optimality conditions and duality in nondifferentiable interval-valued programming
Scalarization of approximate solution for vector equilibrium problems
1. | Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China |
2. | Department of Mathematics, Chongqing Normal University, Chongqing, 400047 |
References:
[1] |
Q. H. Ansari, W. Oettli and D. Schager, A generalization of vectorial equilibria,, Mathematical Methods of Operations Research, 46 (1997), 147.
|
[2] |
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. |
[3] |
M. Bianchi, N. Hadjisawas and S. Schaible, Vector equilibrium problems with generalized monotone bifunctions,, J. Optim. Theory Appl., 92 (1997), 527.
doi: 10.1023/A:1022603406244. |
[4] |
J. P. Dauer and R. J. Gallagher, Positive proper efficient points and related cone results in vector optimization theory,, SIAM J. Control Optim., 28 (1990), 158.
doi: 10.1137/0328008. |
[5] |
J. Fu, Simultaneous vector variational inequalities and vector implicit complementarity problems,, J. Optim. Theory Appl., 93 (1997), 141.
doi: 10.1023/A:1022653918733. |
[6] |
C. Gerth and P. Weidner, Nonconvex separation theorem and some applications in vector optimization., J. Optim. Theory Appl., 67 (1990), 297.
|
[7] |
X. H. Gong, Efficiency and Henig efficiency for vector equilibrium problems,, J. Optim. Theory Appl., 108 (2001), 139.
|
[8] |
X. H. Gong, Connectedness of the set of efficient solution for generalized systems,, J. Optim. Theory Appl., 138 (2008), 189.
|
[9] |
X. H. Gong, Optimality conditions for vector equilibrium problems,, J. Math. Anal. Appl., 342 (2008), 1455.
|
[10] |
X. H. Gong, W. T. Fu and W. Liu, Super efficiency for a vector equilibrium in locally convex topological vector spaces,, in, (2000), 233.
|
[11] |
X. H. Gong and J. C. Yao, Lower semicontinuity of the set of efficient solutions for generalized systems,, J. Optim. Theory Appl., 138 (2008), 197.
doi: 10.1007/s10957-008-9379-1. |
[12] |
N. Hadjisawas and S. Schaile, From scalar to vector equilibrium problems in the quasimonotone case,, J. Optim. Theory Appl., 96 (1998), 297.
doi: 10.1023/A:1022666014055. |
[13] |
J. Jahn, "Mathematical Vector Optimization in Partially Order Linear Spaces,", Verlag Peter Lang, (1986).
|
[14] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems,, Taiwanese J. Mathematics, 12 (2008), 649.
|
[15] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems,, J. Global Optim., 41 (2008), 187.
doi: 10.1007/s10898-007-9210-9. |
[16] |
Q. S. Qiu, Optimality conditions for vector equilibrium problems with constraints,, J. Industrial Management Optim., 5 (2009), 783.
|
[17] |
J. H. Qiu, Scalarization of Henig properly efficient points in locally convex spaces,, J. Optim. Theory Appl., 147 (2010), 71.
|
show all references
References:
[1] |
Q. H. Ansari, W. Oettli and D. Schager, A generalization of vectorial equilibria,, Mathematical Methods of Operations Research, 46 (1997), 147.
|
[2] |
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. |
[3] |
M. Bianchi, N. Hadjisawas and S. Schaible, Vector equilibrium problems with generalized monotone bifunctions,, J. Optim. Theory Appl., 92 (1997), 527.
doi: 10.1023/A:1022603406244. |
[4] |
J. P. Dauer and R. J. Gallagher, Positive proper efficient points and related cone results in vector optimization theory,, SIAM J. Control Optim., 28 (1990), 158.
doi: 10.1137/0328008. |
[5] |
J. Fu, Simultaneous vector variational inequalities and vector implicit complementarity problems,, J. Optim. Theory Appl., 93 (1997), 141.
doi: 10.1023/A:1022653918733. |
[6] |
C. Gerth and P. Weidner, Nonconvex separation theorem and some applications in vector optimization., J. Optim. Theory Appl., 67 (1990), 297.
|
[7] |
X. H. Gong, Efficiency and Henig efficiency for vector equilibrium problems,, J. Optim. Theory Appl., 108 (2001), 139.
|
[8] |
X. H. Gong, Connectedness of the set of efficient solution for generalized systems,, J. Optim. Theory Appl., 138 (2008), 189.
|
[9] |
X. H. Gong, Optimality conditions for vector equilibrium problems,, J. Math. Anal. Appl., 342 (2008), 1455.
|
[10] |
X. H. Gong, W. T. Fu and W. Liu, Super efficiency for a vector equilibrium in locally convex topological vector spaces,, in, (2000), 233.
|
[11] |
X. H. Gong and J. C. Yao, Lower semicontinuity of the set of efficient solutions for generalized systems,, J. Optim. Theory Appl., 138 (2008), 197.
doi: 10.1007/s10957-008-9379-1. |
[12] |
N. Hadjisawas and S. Schaile, From scalar to vector equilibrium problems in the quasimonotone case,, J. Optim. Theory Appl., 96 (1998), 297.
doi: 10.1023/A:1022666014055. |
[13] |
J. Jahn, "Mathematical Vector Optimization in Partially Order Linear Spaces,", Verlag Peter Lang, (1986).
|
[14] |
K. Kimura and J. C. Yao, Sensitivity analysis of vector equilibrium problems,, Taiwanese J. Mathematics, 12 (2008), 649.
|
[15] |
K. Kimura and J. C. Yao, Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems,, J. Global Optim., 41 (2008), 187.
doi: 10.1007/s10898-007-9210-9. |
[16] |
Q. S. Qiu, Optimality conditions for vector equilibrium problems with constraints,, J. Industrial Management Optim., 5 (2009), 783.
|
[17] |
J. H. Qiu, Scalarization of Henig properly efficient points in locally convex spaces,, J. Optim. Theory Appl., 147 (2010), 71.
|
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