A self-adaptive inertial subgradient extragradient algorithm for solving bilevel equilibrium problems

In this paper, we introduce an inertial subgradient extragradient method with a self-adaptive technique for solving bilevel equilibrium problem in real Hilbert spaces. The algorithm is designed such that its stepsize is chosen without the need for prior estimates of the Lipschitz-like constants of t...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2023-11, Vol.72 (7), p.3637-3658
Main Authors: Jolaoso, Lateef Olakunle, Aremu, Kazeem Olalekan, Oyewole, Olawale Kazeem
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Applications of Mathematics
Geometry
Hilbert space
Mathematics
Mathematics and Statistics
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Summary:In this paper, we introduce an inertial subgradient extragradient method with a self-adaptive technique for solving bilevel equilibrium problem in real Hilbert spaces. The algorithm is designed such that its stepsize is chosen without the need for prior estimates of the Lipschitz-like constants of the upper level bifunction nor a line searching procedure. This provides computational advantages to the algorithm compared with other similar methods in the literature. We prove a strong convergence result for the sequences generated by our algorithm under suitable conditions. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-022-00845-5