| تعداد نشریات | 32 |
| تعداد شمارهها | 861 |
| تعداد مقالات | 8,364 |
| تعداد مشاهده مقاله | 53,004,003 |
| تعداد دریافت فایل اصل مقاله | 9,367,027 |
An improved inertial subgradient extragradient algorithm for pseudomonotone equilibrium problems and its applications | ||
| Journal of Mathematical Modeling | ||
| مقاله 3، دوره 13، شماره 2، مرداد 2025، صفحه 263-280 اصل مقاله (258.73 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.28107.2479 | ||
| نویسندگان | ||
| Bochra Zeghad* 1؛ Nourreddine Daili2 | ||
| 1Laboratory of Fundamental and Numerical Mathematics LMFN, Department of Mathematics, Ferhat Abbas University Setif-1, Setif, Algeria | ||
| 2Department of Mathematics, Ferhat Abbas University Setif-1, Setif, Algeria | ||
| چکیده | ||
| This paper presents an improvement of the inertial subgradient extragradient algorithm by using two non-monotonic step size criterion for pseudomonotone equilibrium problems in real Hilbert spaces. A strong convergence theorem of the suggested algorithm is proved under suitable assumptions on the equilibrium bifunction and the control parameters. Finally, application and numerical example are given, which demonstrate the advantages and efficiency of the proposed algorithm. | ||
| کلیدواژهها | ||
| Equilibrium problem؛ variational inequality؛ inertial method؛ strong convergence؛ subgradient extragradient method | ||
| مراجع | ||
|
[1] P.N. Anh, L.T.H, An, The subgradient extragradient method extended to equilibrium problems, Optimization. 64 (2012) 225–248. [2] A.S. Anikin, A.V. Gasnikov, A.Y. Gornov, Randomization and sparsity in huge-scale optimization problems on the example of the mirror descent method, https://doi.org/10.48550/arXiv.1602.00594, 2016. [3] E. Blum, W. Oettli, From optimization and variational inequality to equilibrium problems, Math. Stud. 63 (1994) 127–149. [4] K. Fan, A minimax inequality and applications, In: O. Shisha, (ed.) Inequalities III, pp. 103–113. Academic Press, San Diego, 1972. [5] S.D. Flam, A.S. Antipin, Equilibrium programming using proximal-like algorithms, Math. Pro- gram. 78 (1996) 29–41. [6] D.V. Hieu, A. Gibali, Strong convergence of inertial algorithms for solving equilibrium problems, Optim. Lett. 14 (2020) 1817–1843. [7] D.V. Hieu, Halpern subgradient extragradient method extended to equilibrium problems, Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat. 111 (2016) 823–840. [8] A.N. Iusem. G. Kassay, W. Sosa, On certain conditions for the existence of solutions of equilibrium problems, Math. Prog. 116 (2009) 259–273. [9] I. Konnov, Combined Relaxation Methods for Variational Inequalities, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 2001. [10] I. Konnov, Equilibrium Models and Variational Inequalities, Mathematics in Science and Engineer- ing, Elsevier, Amsterdam, 2007. [11] L.J. Lin, S. Park, On some generalized quasi-equilibrium problems, J. Math. Anal. Appl. 224 (1998) 167–181. [12] S.I. Lyashko, V.V. Semenov, A new two-step proximal algorithm of solving the problem of equilib- rium programming, In: Goldengorin B (ed) Optimization and its applications in control and data sciences, Springer, Cham, 115 (2016) 315–325. [13] A. Moudafi, Proximal point algorithm extended to equilibrium problems, J. Nat. Geom. 15 (1999) 91–100. [14] L.D. Muu, W. Oettli, Convergence of an adaptive penalty scheme for finding constrained equilibria, Nonlinear Anal. 18 (1992) 1159–1166. [15] M.A. Noor, Hemiequilibrium problems, J. Appl. Math. Stoch. Anal. 2004 (2004) 235–244. [16] M.A. Noor, Invex equilibrium problems, J. Math. Anal. Appl. 302 (2005) 463–475. [17] M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymp- totically nonexpansive mappings, Math. Comput. Model. 32 (2000) 1181–1191. [18] B. Panyanak, C. Khunpanuk, N. Pholasa, et al. Dynamical inertial extragradient techniques for solving equilibrium and fixed-point problems in real Hilbert spaces, J. Inequal. Appl. 2023 (2023) 7. [19] H. ur Rehman, H. Kumam, Y.J. Cho , et al. Weak convergence of explicit extragradient algorithms for solving equilibrium problems, J. Inequal. Appl. 2019 (2019) 282. [20] P. Santos, S. Scheimberg, An inexact subgradient algorithm for equilibrium problems, Comput. Appl. Math. 30 (2011) 91–107. [21] B. Tan, S. Li, Adaptive inertial subgradient extragradient methods for finding minimum-norm so- lutions of pseudomonotone variational inequalities, J. Ind. Manag. Optim. 19 (2023) 7640–7659. [22] B. Tan, S. Cho, J.C. Yao, Accelerated inertial subgradient extragradient algorithms with non- monotonic step sizes for equilibrium problems and fixed point problems, J. Nonlinear Var. Anal. 6 (2022) 89–122. [23] D.Q. Tran, M.L. Dung, V.H. Nguyen, Extragradient algorithms extended to equilibrium problems, Optim. 57 (2008) 749–776. [24] D.V. Thong, P. Cholamjiak, M.T. Rassias, Y.J. Cho, Strong convergence of inertial subgradient extragradient algorithm for solving pseudomonotone equilibrium problems, Optim. Lett. 16 (2021) 545–573. [25] J. van Tiel, Convex Analysis: An Introductory Text, John Wiley Sons, Inc., New York, 1984. [26] N.T. Vinh, L.D. Muu, Inertial extragradient algorithms for solving equilibrium problems, Acta Math. Vietnam. 44 (2019) 639–663. [27] H. K. Xu, Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl. 150 (2011) 360–378. [28] H.K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc. 66 (2002) 240–256. | ||
|
آمار تعداد مشاهده مقاله: 717 تعداد دریافت فایل اصل مقاله: 343 |
||