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Asymptotic strong duality
Bilevel mixed equilibrium problems in Banach spaces : existence and algorithmic aspects
1. | Department of Economics, Ibn Zohr University, B.P. 8658 Poste Dakhla, Agadir, Morocco |
2. | Department of Mathematics, Ibn Zohr University, Agadir, Morocco |
3. | Kaohsiung Medical University, Kaohsiung Medical University, Kaohsiung 80708 |
References:
[1] |
A. S. Antipin, The fixed points of extremal maps: computation by gradient methods, Zh. Vychisl. Mat. Mat. Fiz., 37 (1997), 42-53. |
[2] |
C. Baiocchi and A. Capelo, "Variational and Quasivariational Inequalites: Applications to Free Boundary Problems," John Wiley and Sons, New York, 1984. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, The Mathematics Student, 63 (1994), 123-145. |
[4] |
O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities, J. Optim. Theory. Appl., 105 (2000), 299-323.
doi: 10.1023/A:1004657817758. |
[5] |
G. Cohen, Auxiliary problem principle and decomposition of optimization problems, J. Optim. Theory. Appl., 32 (1980), 277-305.
doi: 10.1007/BF00934554. |
[6] |
G. Cohen, Auxiliary problem principle extended to variational inequalities, J. Optim. Theory. Appl., 59 (1988), 325-333. |
[7] |
X. P. Ding, Auxiliary principle and algorithm for mixed equilibrium problems and bilevel mixed equilibrium problems in Banach spaces, J. Optim. Theory. Appl., 146 (2010), 347-357.
doi: 10.1007/s10957-010-9651-z. |
[8] |
K. Goebel and W. A. Kirk, "Topics in Metric Fixed Point Theory," Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1990. |
[9] |
I. V. Konnov, Generalized monotone equilibrium problems and variational inequalities, in "Handbook of Generalized Convexity and Generalized Monotonicity " (eds. N. Hadjisavvas, S. Koml\'osi and S. Schaible), Springer-Verlag, (2005), 559-618. |
[10] |
A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems, J. Glob. Optim., 47 (2010), 287-292.
doi: 10.1007/s10898-009-9476-1. |
[11] |
M. Patriksson, "Nonlinear Programming and Variational Inequality Problems: a unified approach," Kluwer, Dordrecht, 1999. |
[12] |
E. Zeidler, "Nonlinear Functional Analysis ans Its Applications II/B. Nonlinear Monotone Operators," Springer-Verlag, New York, 1990. |
show all references
References:
[1] |
A. S. Antipin, The fixed points of extremal maps: computation by gradient methods, Zh. Vychisl. Mat. Mat. Fiz., 37 (1997), 42-53. |
[2] |
C. Baiocchi and A. Capelo, "Variational and Quasivariational Inequalites: Applications to Free Boundary Problems," John Wiley and Sons, New York, 1984. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, The Mathematics Student, 63 (1994), 123-145. |
[4] |
O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities, J. Optim. Theory. Appl., 105 (2000), 299-323.
doi: 10.1023/A:1004657817758. |
[5] |
G. Cohen, Auxiliary problem principle and decomposition of optimization problems, J. Optim. Theory. Appl., 32 (1980), 277-305.
doi: 10.1007/BF00934554. |
[6] |
G. Cohen, Auxiliary problem principle extended to variational inequalities, J. Optim. Theory. Appl., 59 (1988), 325-333. |
[7] |
X. P. Ding, Auxiliary principle and algorithm for mixed equilibrium problems and bilevel mixed equilibrium problems in Banach spaces, J. Optim. Theory. Appl., 146 (2010), 347-357.
doi: 10.1007/s10957-010-9651-z. |
[8] |
K. Goebel and W. A. Kirk, "Topics in Metric Fixed Point Theory," Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1990. |
[9] |
I. V. Konnov, Generalized monotone equilibrium problems and variational inequalities, in "Handbook of Generalized Convexity and Generalized Monotonicity " (eds. N. Hadjisavvas, S. Koml\'osi and S. Schaible), Springer-Verlag, (2005), 559-618. |
[10] |
A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems, J. Glob. Optim., 47 (2010), 287-292.
doi: 10.1007/s10898-009-9476-1. |
[11] |
M. Patriksson, "Nonlinear Programming and Variational Inequality Problems: a unified approach," Kluwer, Dordrecht, 1999. |
[12] |
E. Zeidler, "Nonlinear Functional Analysis ans Its Applications II/B. Nonlinear Monotone Operators," Springer-Verlag, New York, 1990. |
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