An alternated inertial general splitting method with linearization for the split feasibility problem

Abstract

In this paper, we propose an alternated inertial general splitting method with linearization for a split feasibility problem. Four rules of inertial parameters and relaxation parameters are discussed, where the adaptive inertial parameters are firstly investigated. The convergence of the proposed method is established under standard conditions. The numerical examples are presented to test four choices of the parameters and illustrate the advantage of our methods. An application in signal processing is presented to illustrate the recovery of the proposed algorithm for the sparse signal.

Keywords:

• Split feasibility problem
• alternated inertial general splitting method with linearization
• general splitting methods with linearization
• alternated inertial CQ algorithm

2010 Mathematics Subject Classifications:

• 47H05
• 47J20
• 47J25
• 65K15
• 90C25

Acknowledgments

We express our thanks to anonymous referees for their constructive suggestions, which significant improved the presentation of this article.

Disclosure statement

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

Additional information

Funding

The first and second authors were supported by the Scientific Research Project of Tianjin Municipal Education Commission [grant number 2020ZD02]. The third author was supported by the National Natural Science Foundation of China [grant number 11401152].