subgradient extragradient algorithm with inertial effects for solving equilibrium problems

[1] Agwu, I. K. and Igbokwe, D. I., 2023. New Iteration Algorithms for Solving Equilibrium Problems and Fixed Point Problems of Two Finite Families of Asymptotically Demicontractive Multivalued Mappings. Sahand Comm. Math. Anal. 20(2), pp.1–38. doi:10.22130/scma.2022.531263.939
[2] Alvarez, F. and Attouch, H., 2001. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set­Valued Var. Anal., 9(1), pp.3–11. doi: 10.1023/A:1011253113155
[3] Asad, M., 2023. A new inertial algorithm for equilibrium problem and a family of nonexpansive operators in Hilbert space. Mathematical Methods in the Applied Sciences, pp. 1–12. doi:
10.1002/mma.9447
[4] Bauschke, H.H. and Combettes, P.L., 2011. Convex Analysis and Monotone Operator Theory in
Hilbert Spaces. CMS books in mathematics, 10, pp.1–978.
[5] Blum, E. and Oettli, W., 1994. From optimization and variational inequality to equilibrum problems.The Mathematics Student, 63(1), pp.127–149.
[6] Censor, Y., Gibali, A. and Reich, S., 2011. The subgradient extragradient method for solving variational inequalities in Hilbert space. J. Optim. Theory Appl, 148(2), pp. 318–335. doi: 10.1007/s10957­010­9757­3
[7] Chidume, Ch., 2009. Geometric Properties of Banach Spaces and Nonlinear Iterations. Lecture Notes in Mathematics, vol. 1965, Springer, Berlin,
[8] Dong, Q. L., Lu, Y. Y. and Yang, J., 2016. The extragradient algorithm with inertial effects for solving the variational inequality. Optimization, 65(12), pp. 2217–2226. doi:
10.1080/02331934.2016.1239266
[9] Fabian, M., Habala, P., Ha′ jek, P., Montesinos, V. and Zizler, V., 2011.Banach Space Theory: The
Basis for Linear and Nonlinear Analysis. CMS Books in Mathematics, (Vol. 1). New York: Springer.
[10] Giannessi, F., Maugeri, A. and Pardalos, P.M., 2001.Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. (vol. 58). Springer Science & Business,
[11] Gibali, A. and Van Hieu, D., 2019. A new inertial double­projection method for solving variational inequalities. J. Fixed Point Theory Appl, 21(4), pp.97. doi: doi.org/10.1007/s11784­019­0726­7.
[12] Hieu, D. and Thong, D. V., 2018. New extragradient­like algorithms for strongly pseudomonotone variational inequalities. J. Global Optim, 70(10), pp. 385–399. doi: 10.1007/s10898­017­0564­3
[13] Hoai, P.T., Thuong, N.T. and Vinh, Nguyen The, 2021. Golden ratio algorithms for solving equilibrium problems in Hilbert spaces. J. Nonlinear Var. Anal. , 5(4), pp.493­518. doi:
10.23952/jnva.5.2021.4.01
[14] Jouymandi, Z. and Moradlou, F., 2018. Retraction algorithms for solving variational inequalities, pseudomonotone equilibrium problems and fixed­point problems in Banach spaces. Numer. Algor, 78,pp.1153–1182. doi: 10.1007/s11075­017­0417­7
[15] Kassay, G., Hai, T.N. and Vinh, N. T., 2018. Coupling Popov’s algorithm with subgradient extragradient method for solving equilibrium problems. J. Nonlinear Convex Anal, 19(6), pp. 959–986.
[16] Kassay, G., Reich, S. and Sabach, S., 2011. Iterative methods for solving systems of variational
inequalities in reflexive Banach spaces. SIAM J. Optim, 21(4), pp.1319–1344. doi: 10.1137/110820002
[17] Korpelevich, G.M., 1976. The extragradient method for finding saddle points and other problems.Ekon. Mat. Metody, 12(4), pp. 747–756.
[18] Maugeri, A. and Raciti, F., 2009. On existence theorems for monotone and nonmonotone variational inequalities. J. Convex Anal, 16(3&4), pp. 899–911.
[19] Nesterov, Y., 1983. A method for solving the convex programming problem with convergence rate O(1/k2), Dokl. Akad. Nauk SSSR, 269, pp. 543–547.
[20] Polyak, B. T., 1964. Some methods of speeding up the convergence of iteration methods. U. S. S. R. Comput. Math. Math. Phys, 4(5), pp. 1–17.
[21] Rockafellar, R.T. and Wets, R.J.B., 2009. Variational analysis (Vol. 317). Springer Science & Business Media.
[22] Safari, M. and Moradlou, F., 2021. Shrinking hybrid method for multiple­sets split feasibility problems and variational inequality problems. Ric. Mat.,pp 1–26. doi: 10.1007/s11587­021­00676­z
[23] Safari, M., Moradlou, F. and Khalilzadeh, A. A., 2022. Hybrid proximal point algorithm for
solving split equilibrium problems and its applications. Hacet. J. Math. Stat, 51(4), pp. 932–957.
doi:10.15672/hujms.1023754
[24] Thong, D. V., Reich, S., Shehu, Y and Iyiola, O. S., 2023. Novel projection methods for solving
variational inequality problems and applications. Numerical Algorithms, 93(3), pp. 1105–1135. doi: 10.1007/s11075­022­01457­x
[25] Tran, D. Q., Muu, L. D. and V. H. Nguyen., 2008. Extragradient algorithms extended to equilibrium problems. Optimization, 57(6), pp. 749–776. doi: 10.1080/02331930601122876
[26] Vuong, P. T., Strodiot, J. J. and Nguyen, V. H., 2013. On extragradient­viscosity methods for solving equilibrium and fixed point problems in a Hilbert space. Optimization, 64, pp. 429–451. doi:10.1080/02331934.2012.759327
[27] Xu, H. K., 2010. Iterative methods for the split feasibility problem in infinite­dimensional Hilbert spaces. Inverse Problems, 26(10), pp. 1–17. doi: 10.1088/0266­5611/26/10/105018
[28] Zarantonello, E. H., 1971. Projections on convex sets in Hilbert space and spectral theory. Contributions to Nonlinear Functional Analysis. Academic, New York, pp. 237–424. doi: 10.1016/B978­0­12­775850­3.50013­3