Halpern inertial subgradient extragradient algorithm for solving equilibrium problems in Banach spaces

In this work, we study an equilibrium problem involving a pseudomonotone bifunction in the context of uniformly smooth and 2-uniformly convex real Banach spaces. For the purpose of solving the fixed point problem of a finite family of multi-valued relatively nonexpansive mappings and the pseudomonot...

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Veröffentlicht in:Applicable analysis Jg. 104; H. 2; S. 314 - 335
1. Verfasser: Abass, H. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 22.01.2025
Taylor & Francis Ltd
Schlagworte:
Adaptive algorithms
Algorithms
Banach spaces
Equilibrium problem
fixed point problem
Fixed points (mathematics)
Iterative algorithms
Iterative methods
pseudomonotone operator
relatively nonexpansive mapping
subgradient extragradient method
ISSN:0003-6811, 1563-504X
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Zusammenfassung:In this work, we study an equilibrium problem involving a pseudomonotone bifunction in the context of uniformly smooth and 2-uniformly convex real Banach spaces. For the purpose of solving the fixed point problem of a finite family of multi-valued relatively nonexpansive mappings and the pseudomonotone equilibrium problem, we introduce an inertial subgradient extragradient method and establish its strong convergence. To increase the step size and enhance the performance of our iterative method, we use a new parameter that is independent of the inertial extrapolation method. We point out that our step size is chosen in a self-adaptive manner, making it simple to calculate our iterative algorithm without having to know the Lipschitz constants beforehand. Finally, we give some numerical results for the proposed algorithm and comparison with some other known algorithms.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2024.2360507