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A family of extragradient methods for solving equilibrium problems
1. | Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Vietnam, Vietnam, Vietnam, Vietnam |
References:
[1] |
J. Bello Cruz, P. Santos and S. Scheimberg, A two-phase algorithm for a variational inequality formulation of equilibrium problems, J. Optim. Theory Appl., 159 (2013), 562-575.
doi: 10.1007/s10957-012-0181-8. |
[2] |
G. Bigi, M. Castellani, M. Pappalardo and M. Passacantando, Existence and solution methods for equilibria, Eur. J. Oper. Research, 227 (2013), 1-11.
doi: 10.1016/j.ejor.2012.11.037. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145. |
[4] |
F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols I and II, Springer-Verlag, New York, 2003. |
[5] |
A. Heusinger and C. Kanzow, Relaxation methods for generalized Nash equilibrium problems with inexact line search, J. Optim. Theory Appl., 143 (2009), 159-183.
doi: 10.1007/s10957-009-9553-0. |
[6] |
K. Fan, A minimax inequality and applications, in Inequality III (ed. O. Shisha), Academic Press, (1972), 103-113. |
[7] |
E. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems, USSR Comput. Math. Math. Phys., 27 (1987), 1462-1473. |
[8] |
I. Konnov, Equilibrium Models and Variational Inequalities, Elsevier, Amsterdam, 2007. |
[9] |
G. Korpelevich, The extragradient method for finding saddle points and other problems, Matecon, 12 (1976), 747-756. |
[10] |
J. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications, Environmental Modeling and Assessment, 5 (2000), 63-73. |
[11] |
G. Mastroeni, On auxiliary principle for equilibrium problems, in Equilibrium Problems and Variational Models (eds. P. Daniele, F. Giannessi and A. Maugeri), Kluwer Academic Publishers, Dordrecht, 68 (2003), 289-298.
doi: 10.1007/978-1-4613-0239-1_15. |
[12] |
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993.
doi: 10.1007/978-94-011-2178-1. |
[13] |
T. T. V. Nguyen, J. J. Strodiot and V. H. Nguyen, The interior proximal extragradient method for solving equilibrium problems, J. Glob. Optim., 44 (2009), 175-192.
doi: 10.1007/s10898-008-9311-0. |
[14] |
T. T. V. Nguyen, J. J. Strodiot and V. H. Nguyen, A bundle method for solving equilibrium problems, Math. Program., 116 (2009), 529-552.
doi: 10.1007/s10107-007-0112-x. |
[15] |
J. Nocedal and S. Wright, Numerical Optimization, Springer, New York, 2006. |
[16] |
, Optimization Toolbox User's Guide. For Use with MATLAB, The Math Works Inc., 2014. |
[17] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. |
[18] |
J. J. Strodiot, T. T. V. Nguyen and V. H. Nguyen, A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems, J. Global Optim., 56 (2013), 373-397.
doi: 10.1007/s10898-011-9814-y. |
[19] |
D. Q. Tran, L. D. Muu and V. H. Nguyen, Extragradient algorithms extended to equilibrium problems, Optimization, 57 (2008), 749-776.
doi: 10.1080/02331930601122876. |
[20] |
D. Zaporozhets, A. Zykina and N. Melen'chuk, Comparative analysis of the extragradient methods for solution of the variational inequalities of some problems, Automation and Remote Control, 73 (2012), 626-636.
doi: 10.1134/S0005117912040030. |
[21] |
A. Zykina and N. Melen'chuk, A two-step extragradient method for variational inequalities, Russian Mathematics, 54 (2010), 71-73.
doi: 10.3103/S1066369X10090082. |
[22] |
A. Zykina and N. Melen'chuk, A doublestep extragradient method for solving a resource management problem, Modeling and Analysis of Information Systems, 17 (2010), 65-75. |
[23] |
A. Zykina and N. Melen'chuk, A doublestep extragradient method for solving a problem of the management of resources, Automatic Control and Computer Science, 45 (2011), 452-459.
doi: 10.3103/S0146411611070170. |
[24] |
A. Zykina and N. Melen'chuk, Convergence of the two-step extragradient method in a finite number of iterations, III International Conference: Optimization and Applications, Optima-2012, Costa da Caparica, Portugal, (2012), 23-30. |
show all references
References:
[1] |
J. Bello Cruz, P. Santos and S. Scheimberg, A two-phase algorithm for a variational inequality formulation of equilibrium problems, J. Optim. Theory Appl., 159 (2013), 562-575.
doi: 10.1007/s10957-012-0181-8. |
[2] |
G. Bigi, M. Castellani, M. Pappalardo and M. Passacantando, Existence and solution methods for equilibria, Eur. J. Oper. Research, 227 (2013), 1-11.
doi: 10.1016/j.ejor.2012.11.037. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145. |
[4] |
F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols I and II, Springer-Verlag, New York, 2003. |
[5] |
A. Heusinger and C. Kanzow, Relaxation methods for generalized Nash equilibrium problems with inexact line search, J. Optim. Theory Appl., 143 (2009), 159-183.
doi: 10.1007/s10957-009-9553-0. |
[6] |
K. Fan, A minimax inequality and applications, in Inequality III (ed. O. Shisha), Academic Press, (1972), 103-113. |
[7] |
E. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems, USSR Comput. Math. Math. Phys., 27 (1987), 1462-1473. |
[8] |
I. Konnov, Equilibrium Models and Variational Inequalities, Elsevier, Amsterdam, 2007. |
[9] |
G. Korpelevich, The extragradient method for finding saddle points and other problems, Matecon, 12 (1976), 747-756. |
[10] |
J. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications, Environmental Modeling and Assessment, 5 (2000), 63-73. |
[11] |
G. Mastroeni, On auxiliary principle for equilibrium problems, in Equilibrium Problems and Variational Models (eds. P. Daniele, F. Giannessi and A. Maugeri), Kluwer Academic Publishers, Dordrecht, 68 (2003), 289-298.
doi: 10.1007/978-1-4613-0239-1_15. |
[12] |
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993.
doi: 10.1007/978-94-011-2178-1. |
[13] |
T. T. V. Nguyen, J. J. Strodiot and V. H. Nguyen, The interior proximal extragradient method for solving equilibrium problems, J. Glob. Optim., 44 (2009), 175-192.
doi: 10.1007/s10898-008-9311-0. |
[14] |
T. T. V. Nguyen, J. J. Strodiot and V. H. Nguyen, A bundle method for solving equilibrium problems, Math. Program., 116 (2009), 529-552.
doi: 10.1007/s10107-007-0112-x. |
[15] |
J. Nocedal and S. Wright, Numerical Optimization, Springer, New York, 2006. |
[16] |
, Optimization Toolbox User's Guide. For Use with MATLAB, The Math Works Inc., 2014. |
[17] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. |
[18] |
J. J. Strodiot, T. T. V. Nguyen and V. H. Nguyen, A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems, J. Global Optim., 56 (2013), 373-397.
doi: 10.1007/s10898-011-9814-y. |
[19] |
D. Q. Tran, L. D. Muu and V. H. Nguyen, Extragradient algorithms extended to equilibrium problems, Optimization, 57 (2008), 749-776.
doi: 10.1080/02331930601122876. |
[20] |
D. Zaporozhets, A. Zykina and N. Melen'chuk, Comparative analysis of the extragradient methods for solution of the variational inequalities of some problems, Automation and Remote Control, 73 (2012), 626-636.
doi: 10.1134/S0005117912040030. |
[21] |
A. Zykina and N. Melen'chuk, A two-step extragradient method for variational inequalities, Russian Mathematics, 54 (2010), 71-73.
doi: 10.3103/S1066369X10090082. |
[22] |
A. Zykina and N. Melen'chuk, A doublestep extragradient method for solving a resource management problem, Modeling and Analysis of Information Systems, 17 (2010), 65-75. |
[23] |
A. Zykina and N. Melen'chuk, A doublestep extragradient method for solving a problem of the management of resources, Automatic Control and Computer Science, 45 (2011), 452-459.
doi: 10.3103/S0146411611070170. |
[24] |
A. Zykina and N. Melen'chuk, Convergence of the two-step extragradient method in a finite number of iterations, III International Conference: Optimization and Applications, Optima-2012, Costa da Caparica, Portugal, (2012), 23-30. |
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