Solving Non-monotone Variational Inequality Problems Involving Non-Lipschitz Mappings with Application to Image Restoration.

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Title: Solving Non-monotone Variational Inequality Problems Involving Non-Lipschitz Mappings with Application to Image Restoration.
Authors: Adamu, Abubakar1,2,3 (AUTHOR) adamuabubakar@cqnu.edu.cn, Viet Thong, Duong4 (AUTHOR) thongduongviet@neu.edu.vn, Thi An, Nguyen4 (AUTHOR) annt@neu.edu.vn, Huy Ngan, Dang4 (AUTHOR) ngandh@neu.edu.vn
Source: Journal of Scientific Computing. Jun2026, Vol. 107 Issue 3, p1-30. 30p.
Subjects: Monotone operators, Lipschitz spaces, Hilbert space
Abstract: In this paper, we introduce two self-adaptive subgradient extragradient methods for solving non-monotone variational inequalities involving non-Lipschitz mappings in real Hilbert space. Under weaker conditions than the existing conditions, we investigate and present strong convergence theorems of the proposed algorithms. Our results extend and improve the studied results in the literature. Finally, we give an application to image restoration and some numerical experiments to demonstrate the efficiency of our proposed algorithms. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:In this paper, we introduce two self-adaptive subgradient extragradient methods for solving non-monotone variational inequalities involving non-Lipschitz mappings in real Hilbert space. Under weaker conditions than the existing conditions, we investigate and present strong convergence theorems of the proposed algorithms. Our results extend and improve the studied results in the literature. Finally, we give an application to image restoration and some numerical experiments to demonstrate the efficiency of our proposed algorithms. [ABSTRACT FROM AUTHOR]
ISSN:08857474
DOI:10.1007/s10915-026-03274-z