Modified accelerated Bregman projection methods for solving quasi-monotone variational inequalities

• Published in: Optimization Vol. 73; no. 7; pp. 2053 - 2087
• Main Authors: Wang, Zhong-bao, Sunthrayuth, Pongsakorn, Adamu, Abubakar, Cholamjiak, Prasit
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 15-03-2023; Taylor & Francis LLC
• Subjects: Bregman projection; Convergence; Hilbert space; Image restoration; Inequalities; quasi-monotone mapping; variational inequality problem; weak convergence
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2023.2187663

In this paper, we introduce three new inertial-like Bregman projection methods with a nonmonotone adaptive step-size for solving quasi-monotone variational inequalities in real Hilbert spaces. Under some suitable conditions, the weak convergence of these methods is proved without the prior knowledge of the Lipschitz constant of the operator and the strong convergence of some proposed methods under a strong quasi-monotonicity assumption of the mapping is also provided. Finally, several numerical experiments and applications in image restoration problems are provided to illustrate the performance of the proposed methods.