Inertial accelerated algorithms for the split common fixed-point problem of directed operators

Abstract

In this paper, we introduce two inertial accelerated algorithms for solving the split common fixed-point problem of directed operators in real Hilbert space. The proposed iterative algorithms combine the primal-dual method and the inertial method with the self-adaptive stepsizes such that the implementation of our algorithms does not need any prior information about bounded linear operator norms. Under suitable conditions, the weak and strong convergence results of the algorithms are obtained. Numerical results which involve image restoration problems are reported to show the effectiveness of the proposed algorithms.

Keywords:

• Split common fixed-point problem
• directed operator
• inertial technique
• self-adaptive algorithm
• weak convergence

AMS Mathematics Subject Classifications:

• 47H09
• 47H10
• 47J05
• 54H25

Acknowledgments

We are sincerely grateful to editor and the anonymous referees for helping us improve the original manuscript.

Disclosure statement

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

Additional information

Funding

Supported by Scientific Research Project of Tianjin Municipal Education Commission [grant number 2020ZD02].