References
- Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math. Student. 1994;63:127–149.
- Muu LD, Oettli W. Convergence of an adaptive penalty scheme for finding constrained equilibria. Nonlinear Anal.: TMA. 1992;18:1159–1166.
- Facchinei F, Pang JS. Finite – dimensional variational inequalities and complementarity problems. New York: Springer; 2003.
- Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekon. Math. Methody. 1976;12:747–756.
- Anh PN, Son DX. A new method for a finite family of pseudocontractions and equilibrium problems. J. Appl. Math. Inf. 2011;29:1179–1191.
- Iusem AN, Swaiter BF. A variant of Korpelevich’s method for variational inequalities with new search strategy. Optimization. 1997;42:309–321.
- Muu LD, Nguyen VH, Quoc TD. Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776.
- Solodov MV, Svaiter BF. A hybrid projection-proximal point algorithm. J. Convex Anal. 1999;6:59–70.
- Solodov MV, Svaiter BF. A new projection method for variational inequality problems. SIAM J. Control. Optim. 1999;37:765–776.
- Tikhonov AN, Arsenin VYa. Solutions of ill-posed problems. New York: John Wiley and Sons; 1977.
- Hung PG, Muu LD. The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions. Nonlinear Anal. 2011;74:6121–6129.
- Konnov IV. Regularization methods for nonmonotone equilibrium problems. J. Nonlinear Convex Anal. 2009;10:93–101.
- Konnov IV, Dyabilkin DA. Nonmonotone equilibrium problems: coercivity and weak regularization. J. Glob. Optim. 2011;49:575–587.
- Liskovets OA. Regularized variational inequalities with pseudomonotone operators on approximately given sets. Differ. Equ. 1989;25:1970–1977.
- Tam NN, Yao JC, Yen ND. Solution methods for pseudomonotone variational inequalities. J. Optim. Theory Appl. 2008;38:253–273.
- Dinh BV, Muu LD. On penalty and gap function methods for bilevel equilibrium problems. J. Appl. Math. 2011;2011, Article ID 646452. doi:10.1155/2011/646452.
- Ding XP. Auxiliary principle and algorithm for mixed equilibrium problems and bilevel equilibrium problems in Banach spaces. J. Optim. Theory Appl. 2010;146:347–357.
- Luo JQ, Pang JS, Ralph D. Mathematical programs with equilibrium constraints. Cambridge (UK): Cambridge University Press; 1996.
- Moudafi A. Proximal methods for a class of bilevel monotone equilibrium problems. J. Glob. Optim. 2010;47:287–292.
- Muu LD, Quy NV. A global optimization method for solving convex quadratic bilevel programming problems. J. Glob. Optim. 2003;26:199–219.
- Tada A, Takahashi W. Weak and strong convergence theorem for nonexpansive mapping and equilibrium problem. J. Optim. Theory Appl. 2007;133:359–370.
- Konnov IV. Combined relaxation methods for variational inequalities. Berlin: Springer-Verlag; 2001.
- Mastroeni G. On auxiliary priciple for equilibrium problems. J. Glob. Optim. 2003;27:411–426.
- Censor Y, Lent A. An iterative row-action method for interval convex programming. J. Optim. Theory Appl. 1981;34:321–353.
- Muu LD, Quoc TD. Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model. J. Optim. Theory Appl. 2009;142:185–204.
- Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
- Berge C. Topological spaces. New York: The MacMillan; 1984.
- Contreras J, Klusch M, Krawczyk JB. Numerical solution to Nash-Cournot equilibria in coupled constraint electricity markets. EEE Trans. Power Syst. 2004;19::195–206.
- Quoc TD, Anh PN, Muu LD. Dual extragradient algorithms extended to equilibrium problems. J. Glob. Optim. 2012;52:139–159.