Accelerated hybrid viscosity and steepest-descent method for proximal split feasibility problems

Abstract

The purpose of this paper is to present an accelerated hybrid viscosity and steepest-descent method for solving proximal split feasibility problems (if solutions exist) in real Hilbert spaces. We obtain strong convergence of the sequence generated by our scheme under some suitable conditions on the parameters. In all our results in this work, our iterative schemes are proposed with a way of selecting the step sizes such that their implementation does not need any prior information about the bounded linear operator norm. Finally, we give numerical comparisons of our results with other established result to verify the efficiency and implementation of our new method.

Keywords:

• Proximal split feasibility problems
• Moreau-Yosida approximate
• strong convergence
• Hilbert spaces

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Alexander von Humboldt-Stiftung [grant number 1163904]