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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.
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.
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.
|
[4] |
F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, Vols I and II, (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.
doi: 10.1007/s10957-009-9553-0. |
[6] |
K. Fan, A minimax inequality and applications,, in Inequality III (ed. O. Shisha), (1972), 103.
|
[7] |
E. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems,, USSR Comput. Math. Math. Phys., 27 (1987), 1462.
|
[8] |
I. Konnov, Equilibrium Models and Variational Inequalities,, Elsevier, (2007).
|
[9] |
G. Korpelevich, The extragradient method for finding saddle points and other problems,, Matecon, 12 (1976), 747.
|
[10] |
J. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications,, Environmental Modeling and Assessment, 5 (2000), 63. Google Scholar |
[11] |
G. Mastroeni, On auxiliary principle for equilibrium problems,, in Equilibrium Problems and Variational Models (eds. P. Daniele, 68 (2003), 289.
doi: 10.1007/978-1-4613-0239-1_15. |
[12] |
A. Nagurney, Network Economics: A Variational Inequality Approach,, Kluwer Academic Publishers, (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.
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.
doi: 10.1007/s10107-007-0112-x. |
[15] |
J. Nocedal and S. Wright, Numerical Optimization,, Springer, (2006).
|
[16] |
, Optimization Toolbox User's Guide. For Use with MATLAB, The Math Works Inc.,, 2014., (). Google Scholar |
[17] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (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.
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.
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.
doi: 10.1134/S0005117912040030. |
[21] |
A. Zykina and N. Melen'chuk, A two-step extragradient method for variational inequalities,, Russian Mathematics, 54 (2010), 71.
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. Google Scholar |
[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.
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, (2012), 23. Google Scholar |
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.
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.
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.
|
[4] |
F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems,, Vols I and II, (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.
doi: 10.1007/s10957-009-9553-0. |
[6] |
K. Fan, A minimax inequality and applications,, in Inequality III (ed. O. Shisha), (1972), 103.
|
[7] |
E. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems,, USSR Comput. Math. Math. Phys., 27 (1987), 1462.
|
[8] |
I. Konnov, Equilibrium Models and Variational Inequalities,, Elsevier, (2007).
|
[9] |
G. Korpelevich, The extragradient method for finding saddle points and other problems,, Matecon, 12 (1976), 747.
|
[10] |
J. Krawczyk and S. Uryasev, Relaxation algorithms to find Nash equilibria with economic applications,, Environmental Modeling and Assessment, 5 (2000), 63. Google Scholar |
[11] |
G. Mastroeni, On auxiliary principle for equilibrium problems,, in Equilibrium Problems and Variational Models (eds. P. Daniele, 68 (2003), 289.
doi: 10.1007/978-1-4613-0239-1_15. |
[12] |
A. Nagurney, Network Economics: A Variational Inequality Approach,, Kluwer Academic Publishers, (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.
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.
doi: 10.1007/s10107-007-0112-x. |
[15] |
J. Nocedal and S. Wright, Numerical Optimization,, Springer, (2006).
|
[16] |
, Optimization Toolbox User's Guide. For Use with MATLAB, The Math Works Inc.,, 2014., (). Google Scholar |
[17] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (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.
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.
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.
doi: 10.1134/S0005117912040030. |
[21] |
A. Zykina and N. Melen'chuk, A two-step extragradient method for variational inequalities,, Russian Mathematics, 54 (2010), 71.
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. Google Scholar |
[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.
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, (2012), 23. Google Scholar |
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