Outer perturbations of a projection method and two approximation methods for the split equality problem

Abstract

In this article, we first present a projection method with outer perturbations for the split equality problem (SEP) and establish its weak convergence. Then combining the proposed projection method with the outer approximation method and Halpern iteration method, we introduce two approximation methods to solve the SEP, where the two closed convex sets are both level sets of convex functions. Finally, a preliminary experiment presented compares the approximation methods and a relaxed projection method.

Keywords:

• Split equality problem
• projection algorithm
• relaxed projection algorithm
• Halpern iteration method
• outer perturbation
• outer approximation method

Acknowledgements

The authors express their thanks to the two anonymous referees and the associate editor, whose careful readings and suggestions led to improvements in the presentation of the results.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [No. 71602144]; Open Fund of Tianjin Key Lab for Advanced Signal Processing [No. 2016ASP-TJ01].