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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 10
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Research Article

Inertial subgradient extragradient method for solving pseudomonotone variational inequality problems in Banach spaces

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Pages 1769-1789 | Received 03 Jun 2023, Accepted 27 Sep 2023, Published online: 21 Oct 2023

References

  • Hartman P, Stampacchia G. On some nonlinear elliptic differential functional equations. Acta Math. 1966;115:271–310. doi: 10.1007/BF02392210
  • Aubin JP, Ekeland I. Applied nonlinear analysis. New York (NY): Courier Corporation; 2006.
  • Clarke FH. Optimization and nonsmooth analysis. Wiley: Society for Industrial and Applied Mathematics; 1990.
  • Ferro F. A minimax theorem for vector-valued functions. J Optim Theory Appl. 1989;60(1):19–31. doi: 10.1007/BF00938796
  • Robinson SM. Regularity and stability for convex multivalued functions. Math Oper Res. 1976;1(2):130–143. doi: 10.1287/moor.1.2.130
  • Yao Y, Noor MA. On viscosity iterative methods for variational inequalities. J Math Anal Appl. 2007;325(2):776–787. doi: 10.1016/j.jmaa.2006.01.091
  • He L, Cui YL, Ceng LC, et al. Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule. J Inequal Appl. 2021;1:1–37.
  • Ceng LC, Petrusel A, Qin X, et al. Pseudomonotone variational inequalities and fixed points. Fixed Point Theory. 2021;22:543–558. doi: 10.24193/fpt-ro
  • Wang DQ, Zhao TY, Ceng LC, et al. Strong convergence results for variational inclusions, systems of variational inequalities and fixed point problems using composite viscosity implicit methods. Optimization. 2022;71:4177–4212. doi: 10.1080/02331934.2021.1939338
  • Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekonomikai Matematicheskie Metody. 1976;12:747–756.
  • Khobotov EN. Modification of the extragradient method for solving variational inequalities and certain optimization problems. Ussr Comput Math Math Phys. 1987;27(5):120–127. doi: 10.1016/0041-5553(87)90058-9
  • Malitsky Y. Projected reflected gradient methods for monotone variational inequalities. SIAM J Optim. 2015;25(1):502–520. doi: 10.1137/14097238X
  • Zaporozhets DN, Zykina AV, Melenchuk NV. Comparative analysis of the extragradient methods for solution of the variational inequalities of some problems. Autom Remote Control. 2012;73(4):626–636. doi: 10.1134/S0005117912040030
  • Denisov SV, Semenov VV, Chabak LM. Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators. Cybern Syst Anal. 2015;51(5):757–765. doi: 10.1007/s10559-015-9768-z
  • Thong DV, Gibali A. Extragradient methods for solving non-Lipschitzian pseudomonotone variational inequalities. J Fixed Point Theory Appl. 2019;21(1):1–19. doi: 10.1007/s11784-018-0656-9
  • Dong QL, Lu YY, Yang JF. The extragradient algorithm with inertial effects for solving the variational inequality. Optimization. 2016;65(12):2217–2226. doi: 10.1080/02331934.2016.1239266
  • Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148(2):318–335. doi: 10.1007/s10957-010-9757-3
  • Kraikaew R, Saejung S. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces. J Optim Theory Appl. 2014;163(2):399–412. doi: 10.1007/s10957-013-0494-2
  • Dong QL, Yuan HB, Cho YJ, et al. Modified inertial Mann algorithm and inertial CQalgorithm for nonexpansive mappings. Optimization Letters. 2018;12(1):87–102. doi: 10.1007/s11590-016-1102-9
  • Dong QL, Cho YJ, Zhong LL, et al. Inertial projection and contraction algorithms for variational inequalities. J Glob Optim. 2018;70(3):687–704. doi: 10.1007/s10898-017-0506-0
  • Yang J, Liu H, Liu Z. Modified subgradient extragradient algorithms for solving monotone variational inequalities. Optimization. 2018;67(12):2247–2258. doi: 10.1080/02331934.2018.1523404
  • Tan B, Li S, Qin X. Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems. Appl Numer Math. 2021;170:219–241. doi: 10.1016/j.apnum.2021.07.022
  • Ceng LC, Zhu LJ, Yin TC. Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints. AIMS Math. 2023;8(2):2961–2994. doi: 10.3934/math.2023154
  • Ceng LC, Petrusel A, Qin X, et al. On inertial subgradient extragradient rule for monotone bilevel equilibrium problems. Fixed Point Theory. 2023;24(1):101–126. doi: 10.24193/fpt-ro
  • Ceng LC, Yao JC, Shehu Y. On Mann implicit composite subgradient extragradient methods for general systems of variational inequalities with hierarchical variational inequality constraints. J Inequal Appl. 2022;1:28.
  • Ceng LC, Petrusel A, Qin X, et al. A modified inertial subgradient extragradient method for solving pseudomonotone variational inequalities and common fixed point problems. Fixed Point Theory. 2020;21:93–108. doi: 10.24193/fpt-ro
  • Ceng LC, Shang M. Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings. Optimization. 2021;70:715–740. doi: 10.1080/02331934.2019.1647203
  • Ceng LC, Petrusel A, Qin X, et al. Two inertial subgradient extragradient algorithms for variational inequalities with fixed-point constraints. Optimization. 2021;70:1337–1358. doi: 10.1080/02331934.2020.1858832
  • Kravchuk AS, Neittaanmaki PJ. Variational and quasi-variational inequalities in mechanics. Germany: Springer Science Business Media; 2007.
  • Cai G, Gibali A, Iyiola OS, et al. A new double-projection method for solving variational inequalities in Banach spaces. J Optim Theory Appl. 2018;178(1):219–239. doi: 10.1007/s10957-018-1228-2
  • Shehu Y. Single projection algorithm for variational inequalities in Banach spaces with application to contact problem. Acta Mathematica Scientia. 2020;40(4):1045–1063. doi: 10.1007/s10473-020-0412-2
  • Oyewole OK, Abass HA, Mebawondu AA, et al. A Tseng extragradient method for solving variational inequality problems in Banach spaces. Numer Algorithms. 2021;89(2):769–789. doi: 10.1007/s11075-021-01133-6
  • Xie ZB, Cai G, Li XX, et al. Self-adaptive subgradient extragradient method for solving pseudomonotone variational inequality problems in Banach spaces. Banach J Math Anal. 2022;16(1):1–18. doi: 10.1007/s43037-021-00152-8
  • Jolaoso LO, Aphane M. An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces. Numer Algorithms. 2021;89(2):583–610. doi: 10.1007/s11075-021-01126-5
  • Taiwo A, Jolaoso LO, Mewomo OT. Inertial-type algorithm for solving split common fixed point problems in Banach spaces. J Sci Comput. 2021;86(1):1–30. doi: 10.1007/s10915-020-01385-9
  • Van HD, Muu LD, Quy PK, et al. New extragradient methods for solving equilibrium problems in Banach spaces. Banach J Math Anal. 2021;15(1):1–24. doi: 10.1007/s43037-020-00085-8
  • Jolaoso LO, Ogbuisi FU, Mewomo OT. On split equality variation inclusion problems in Banach spaces without operator norms. Int J Nonlinear Anal Appl. 2021;12(Special Issue):425–446.
  • Alber YI. Metric and generalized Projection Operators in Banach Spaces: properties and Applications. Functional Anal. In: A. G. Kartsatos, editor. Theory and Applications of Nonlinear Operators of Accretive and monotone Type. New York: Marcel Dekker; 1996. p. 15–50.
  • Ball K, Carlen EA, Lieb EH. Sharp uniform convexity and smoothness inequalities for trace norms. Inventiones Mathematicae. 1994;115(1):463–482. doi: 10.1007/BF01231769
  • Alber YI, Li JL. The connection between the metric and generalized projection operators in Banach spaces. Acta Mathematica Sinica. 2007;23(6):1109–1120. doi: 10.1007/s10114-005-0718-y
  • Aoyama K, Kohsaka F. Strongly relatively nonexpansive sequences generated by firmly nonexpansive-like mappings. Fixed Point Theory Appl. 2014;95(1):1–13.
  • Reich S. A weak convergence theorem for the alternating method with Bregman distances. Theory Appl Nonlinear Oper Accretive Monotone Type. 1996;178:313–318.
  • Iiduka H, Takahashi W. Weak convergence of a projection algorithm for variational inequalities in a Banach space. J Math Anal Appl. 2008;339(1):668–679. doi: 10.1016/j.jmaa.2007.07.019
  • Saejung S, Yotkaew P. Approximation of zeros of inverse strongly monotone operator in Banach spaces. Nonlinear Anal. 2012;75(2):742–750. doi: 10.1016/j.na.2011.09.005
  • Kamimura S, Takahashi W. Strong convergence of a proximal-type algorithm in a Banach space. SIAM J Optim. 2002;13(3):938–945. doi: 10.1137/S105262340139611X
  • Maing PE. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-valued Analysis. 2008;16(7):899–912. doi: 10.1007/s11228-008-0102-z
  • Yang J, Liu H. Strong convergence result for solving monotone variational inequalities in Hilbert space. Numer Algorithms. 2019;80(3):741–752. doi: 10.1007/s11075-018-0504-4

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