On Bilevel Monotone Inclusion and Variational Inequality Problems

Austine Efut Ofem (), Jacob Ashiwere Abuchu, Hossam A. Nabwey (), Godwin Chidi Ugwunnadi and Ojen Kumar Narain
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Austine Efut Ofem: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa
Jacob Ashiwere Abuchu: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa
Hossam A. Nabwey: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Godwin Chidi Ugwunnadi: Department of Mathematics, University of Eswatini, Kwaluseni M201, Eswatini
Ojen Kumar Narain: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa

Mathematics, 2023, vol. 11, issue 22, 1-28

Abstract: In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted.

Keywords: monotone inclusion problem; variational inequality problem; projection and contraction method; Tseng method; strong convergence; inertial term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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