Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 8
237
Views
6
CrossRef citations to date
0
Altmetric
Research Article

Strongly convergent inertial extragradient type methods for equilibrium problems

ORCID Icon, ORCID Icon, &
Pages 2160-2188 | Received 13 Jun 2021, Accepted 08 Dec 2021, Published online: 30 Dec 2021

References

  • Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Program. 1994;63:123–145.
  • Tan B, Cho SY. Strong convergence of inertial forward-backward methods for solving monotone inclusions. Appl Anal. 2021. doi:10.1080/00036811.2021.1892080
  • Konnov IV. Equilibrium models and variational inequalities. Amsterdam: Elsevier; 2007.
  • Muu LD, Oettli W. Convergence of an adaptive penalty scheme for finding constraint equilibria. Nonlinear Anal. 1992;18:1159–1166.
  • Shehu Y, Iyiola OS, Thong DV, et al. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Math Meth Oper Res. 2020. doi:10.1007/s00186-020-00730-w
  • Dadashi V, Iyiola OS, Shehu Y. The subgradient extragradient method for pseudomonotone equilibrium problems. Optimization. 2020;69(4):901–923.
  • Cho SY. A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space. Filomat. 2020;34:1487–1497.
  • Cho SY. A convergence theorem for generalized mixed equilibrium problems and multivalued asymptotically nonexpansive mappings. J Nonlinear Convex Anal. 2020;21:1017–1026.
  • Tan B, Fan J, Li S. Self-adaptive inertial extragradient algorithms for solving variational inequality problems. Comp Appl Math. 2021;40:19.
  • Moudafi A. Second-order differential proximal methods for equilibrium problems. J Inequal Pure Appl Math. 2003;4:18.
  • Nguyen TTV, Strodiot JJ, Nguyen VH. Hybrid methods for solving simultaneously an equilibrium problem and countably many fixed point problems in a Hilbert space. J Optim Theory Appl. 2014;160(3):809–831.
  • Tran DQ, Dung ML, Nguyen VH. Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776.
  • Vinh NT, Muu LD. Inertial extragradient algorithms for solving equilibrium problems. Acta Math Vietnam. 2019;44(3):639–663.
  • Vuong PT, Strodiot JJ, Nguyen VH. On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space. Optimization. 2015;64(2):429–451.
  • Zhu LJ, Yao Y, Postolache M. Projection methods with linesearch technique for pseudomonotone equilibrium problems and fixed point problems. U.P.B. Sci Bull Series A. 2021;83(1):3–14.
  • Shehu Y, Dong Q-L, Jiang D. Single projection method for pseudo-monotone variational inequality in Hilbert spaces. Optimization. 2019;68:385–409.
  • Hieu DV, Strodiot JJ, Muu LD. Strongly convergent algorithms by using new adaptive regularization parameter for equilibrium problems. J Comput Appl Math. 2020;376:1–21.
  • Alvarez F, Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 2001;9:3–11.
  • Hieu DV. New inertial algorithm for a class of equilibrium problems. Numer Algorithms. 2019;80(4):1413–1436.
  • Rehman H, Kumam P, Argyros IK, et al. Inertial extra-Gradient method for solving a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces with application in variational inequality problem. Symmetry. 2020;12:503.
  • Hieu DV, Quy PK, Hong LT, et al. Accelerated hybrid methods for solving pseudomonotone equilibrium problems. Adv Comput Math. 2020;46:58.
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York (NY): Springer; 2011. (CMS Books in Mathematics).
  • Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
  • Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numer Algo. 2020;84:365–388.
  • Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Appl Anal. doi:10.1080/00036811.2020.1736287
  • Yang J, Liu H. The subgradient extragradient method extended to pseudomonotone equilibrium problems and fixed point problems in Hilbert space. Optim Lett. 2020;14:1803–1816.
  • Hieu DV. An inertial-like proximal algorithm for equilibrium problems. Math Meth Oper Res. 2018;88(3):399–415.
  • Vuong PT, Strodiot JJ, Nguyen VH. Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and fixed point problems. J Optim Theor Appl. 2012;155:605–627.
  • Nguyen TTV, Strodiot JJ, Nguyen VH. Hybrid methods for solving simultaneously an equilibrium problem and countably many fixed point problems in a Hilbert space. J Optim Theor Appl. 2014;160:809–831.
  • Pang JS, Facchinei F. Finite-dimensional variational inequalities and complementarity problems. New York (NY): Springer Science and Business Media; 2007.
  • 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.
  • Dinh BV, Kim DS. Projection algorithms for solving nonmonotone equilibrium problems in Hilbert space. J Comput Appl Math. 2016;302:106–117.
  • Quoc TD, Anh PN, Muu LD. Dual extragradient algorithms extended to equilibrium problems. J Global Optim. 2012;52(1):139–159.
  • ur Rehman H, Kumam P, Cho YJ, et al. Modified Popov's explicit iterative algorithms for solving pseudomonotone equilibrium problems. Optim Meth Software. 2021;36:82–113.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.