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

Abstract

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.

Keywords:

• Bregman projection
• Hilbert space
• weak convergence
• variational inequality problem
• quasi-monotone mapping

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by The Science, Research and Innovation Promotion Funding (TSRI) [grant number FRB660012/0168]. This research block grants was managed under Rajamangala University of Technology Thanyaburi [grant number FRB66E0628]. Z.-B. Wang was supported by the National Natural Science Foundation of China (11701479) and the Fundamental Research Funds for the Central Universities (2682021ZTPY040). P. Cholamjiak was supported by University of Phayao and Thailand Science Research and Innovation [grant number FF66-UoE].