Strong convergence result for proximal split feasibility problem in Hilbert spaces

Abstract

In this paper we describe and analyse new computational technique for solving proximal split feasibility problem (SFP) using a modified proximal split feasibility algorithm. The two convex and lower semi-continuous objective functions are assumed to be non-smooth. Some application to SFP are given. We demonstrate the computational efficiency of the proposed algorithm with nontrivial numerical experiments. We also compare our method with other relevant methods in the literature in terms of convergence, stability, efficiency and implementation with our illustrative numerical examples.

Keywords:

• Proximal split feasibility problems
• strong convergence
• numerical analysis
• Hilbert spaces

Acknowledgements

We thank the anonymous referees and the Associate Editor for insightful comments and suggestions which led to great improvement of the first version of the paper. The research was carried out when the First Author was an Alexander von Humboldt Postdoctoral Fellow at the Institute of Mathematics, University of Wurzburg, Germany. He is grateful to the Alexander von Humboldt Foundation, Bonn for the fellowship and the Institute of Mathematics, University of Wurzburg, Germany for the hospitality and facilities.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of this author is supported by the Alexander von Humboldt-Stiftung [grant number 1163904].