References
- Bigi G, Castellani M, Pappalardo M, et al. Existence and solution methods for equilibria. Eur Oper Res. 2013;227:1–11.
- Bigi G, Castellani M, Pappalardo M, et al. Nonlinear programming techniques for equilibria. Springer International Publishing; 2019.
- Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Student. 1994;62:127–169.
- Muu LD, W. Oettli. Convergence of an adaptive penalty scheme for finding constrained equilibria. Nonlinear Anal: TMA. 1992;18:1159–1166.
- Nikaido H, Isoda K. Note on noncooperative convex games. Pacific Math. 1955;5:807–815.
- Fan K. A minimax inequality and applications. In: Shisha O, editor. Inequalities. New York (NY): Academic Press; 1972. p. 103–113.
- Aussel D. Adjusted sublevel sets, normal operator and quasiconvex programming. SIAM J Optim. 2005;16:358–367.
- Aussel D, Dutta J, Pandit T. About the links between equilibrium problems and variational inequalities. In: Neogy SK, Bapat RB, Dubey D, editors. Mathematical programming and game theory. Singapore: Springer; 2018. p. 115–130.
- Hieu DV, Quy PK, Vy LV. Explicit iterative algorithms for solving equilibrium problems. Calcolo. 2019;56:11. doi:10.1007/s10092-019-0308-5.
- Ramirez LM, Papa Quiroz EA, Oliveira PR. An inexact proximal method with proximal distances for quasimonotone equilibrium problems. J Oper Res Soc China. 2017;5:545–561.
- 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.
- Langenberg N. Interior point methods for equilibrium problems. Comput Optim Appl. 2012;53:453–483.
- Papa Quiroz EA, Ramirez LM, Oliveira PR. An inexact algorithm with proximal distances for variational inequalities. RAIRO-Oper Res. 2018;52(1):159–176.
- Quoc TD, Muu LD, Nguyen VH. Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776.
- Santos P, Scheimberg S. An inexact subgradient algorithm for equilibrium problems. Comput Appl Math. 2011;30:91–107.
- Santos P, Scheimberg S. A modified projection algorithm for constrained equilibrium problems. Optimization. 2017;66:2051–2062.
- Thuy LQ, Hai TN. A projected subgradient algorithm for bilevel equilibrium problems and applications. J Optim Theory Appl. 2017;175:411–431.
- Yen LH, Huyen NTT, Muu LD. A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models. J Glob Optim. 2019;73:849–858.
- Cruz Neto JX, Lopes JO, Soares PA. A minimization algorithm for equilibrium problems with polyhedral constraints. Optimization. 2016;65(5):1061–1068.
- Kassay G, Radulesku V. Equilibrium problems and applications. Series Mathematics in Science and Engineering. Academic Press; 2018.
- Cotrina J, Garcia Y. Equilibrium problems: existence results and applications. Set-Valued Anal. 2018;26:159–177.
- Yen LH, Muu LD. A subgradient method for equilibrium problems involving quasiconvex bifunction. Oper Res Lett. 2020;48(5):579–583.
- Mangasarian O. Nonlinear programming. New York (NY): McGraw-Hill; 1969.
- Aussel D. New development of convex optimization. In: Fixed point theory variational analysis and optimizationTaylor and Francis; 2014. p. 173–208.
- Penot J-P. Are generalized derivatives useful for generalized convex functions? In: Crouzeix J-P, Martinez-Legaz JE, Volle M, editors. Generalized convexity, generalized monotonicity: recent results. Dordrecht: Kluwer Academic Publishers; 1998. p. 3–59.
- Penot J-P, Zalinescu C. Elements of quasiconvex subdifferential calculus. J Convex Anal. 2000;7:243–269.
- Greenberg HP, Pierskalla WP. Quasi-conjugate functions and surrogate duality. Cahiers Centre Études Recherche Oper. 1973;15:437–448.
- Nimanaa N, Farajzadehb AP, Petrot N. Adaptive subgradient method for the split quasiconvex feasibility problems. Optimization. 2016;65:1885–1898.
- Kiwiel KC. Convergence and efficiency of subgradient methods for quasiconvex minimization. Math Program Ser A. 2001;90:1–25.
- Deutsch F, Yamada I. Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer Funct Anal Optim. 1998;19:33–56.
- Gromicho J. Quasiconvex optimization and location theory. Dordrecht: Kluwer Academic Publishers; 1998.
- Iusem AN. On some properties of paramonotone operator. Convex Anal. 1998;5:269–278.
- Konnov I. On convergent properties of a subgradient method. Optim Meth Softw. 2003;17:53–62.
- Anh PN, Muu LD. A hybrid subgradient algorithm for nonexpansive mapping and equilibrium problems. Optim Lett. 2014;8:727–738.
- Duc PM, Muu LD, Quy NV. Solution-existence and algorithms with their convergence rate for strongly pseudomonotone equilibrium problems. Pacific J Optim. 2016;12(4):833–845.
- Duc PM, Muu LD. A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings. Optimization. 2016;65:1855–1866.
- Zhao Y-B. Iterative methods for monotone generalized variational inequalities. Optimization. 1997;42:285–307.
- He B. Algorithm for a class of generalized linear variational inequality and its application. Sci China (Series A). 1995;25:939–945.
- He B, He X-Z, Liu HK. Solving a class of constrained ‘black-box’ inverse variational inequalities. Eur J Oper Res. 2010;204:391–401.
- Rockafellar RT, Wets R. Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. SIAM J Control Optim. 1990;28:810–820.