Modified inertial subgradient extragradient algorithms for generalized equilibria systems with constraints of variational inequalities and fixed points

Lu-Chuan Ceng; Shih-Hsin Chen; Yeong-Cheng Liou; Tzu-Chien Yin; Lu-Chuan Ceng; Shih-Hsin Chen; Yeong-Cheng Liou; Tzu-Chien Yin

doi:10.3934/math.2024672

AIMS Mathematics

2024, Volume 9, Issue 6: 13819-13842. doi: 10.3934/math.2024672

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Modified inertial subgradient extragradient algorithms for generalized equilibria systems with constraints of variational inequalities and fixed points

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2.
Department of Computer Science and Information Engineering, Tamkang University, Taiwan
3.
Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan
4.
Project Management Office for Intelligence Healthcare, and Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan
5.
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 11 February 2024 Revised: 31 March 2024 Accepted: 10 April 2024 Published: 15 April 2024
MSC : 47H09, 47H10, 47J20, 47J25

In this research, we studied modified inertial composite subgradient extragradient implicit rules for finding solutions of a system of generalized equilibrium problems with a common fixed-point problem and pseudomonotone variational inequality constraints. The suggested methods consisted of an inertial iterative algorithm, a hybrid deepest-descent technique, and a subgradient extragradient method. We proved that the constructed algorithms converge to a solution of the considered problem, which also solved some hierarchical variational inequality.
Citation: Lu-Chuan Ceng, Shih-Hsin Chen, Yeong-Cheng Liou, Tzu-Chien Yin. Modified inertial subgradient extragradient algorithms for generalized equilibria systems with constraints of variational inequalities and fixed points[J]. AIMS Mathematics, 2024, 9(6): 13819-13842. doi: 10.3934/math.2024672

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Abstract

In this research, we studied modified inertial composite subgradient extragradient implicit rules for finding solutions of a system of generalized equilibrium problems with a common fixed-point problem and pseudomonotone variational inequality constraints. The suggested methods consisted of an inertial iterative algorithm, a hybrid deepest-descent technique, and a subgradient extragradient method. We proved that the constructed algorithms converge to a solution of the considered problem, which also solved some hierarchical variational inequality.

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