An inertial hyperplane projection method for split feasibility problems and applications

ABSTRACT

In this paper, we propose a new projection algorithm to solve the split feasibility problem in Hilbert spaces. This method involves a new strategy that projects the inertial term onto the intersection of the feasible set and a half-space. The strong and weak convergence of the new algorithms under standard assumptions are established. We examine the performance of our method on sparse signal processing and image deblurring problems. The reported numerical results demonstrate the effectiveness of the proposed algorithm.

KEYWORDS:

• Split feasibility problem
• hyperplane projection method
• CQ algorithm
• weak convergence
• strong convergence

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 90C25

Acknowledgments

The authors would like to thank the editor and the reviewers for their constructive suggestions and comments, which greatly improve the manuscript.

Disclosure statement

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

Additional information

Funding

This research is funded by Hanoi University of Science and Technology (HUST) under project number T2023-PC-081.