Two inertial-type algorithms for solving the split feasibility problem

Abstract

In this paper, we study two inertial-type algorithms with a relaxed splitting method for solving the split feasibility problem in Hilbert spaces. Weak convergence is established without assuming conditions such as $\sum _{k=1}^{\mathrm{\infty }}{\theta }_k\Vert x^k-x^{k-1}{\Vert }^2<\mathrm{\infty }$ and $\sum _{k=1}^{\mathrm{\infty }}\Vert x^k-x^{k-1}{\Vert }^2<\mathrm{\infty }$, where ${\theta }_k$ is the inertial factor. Compared with existing results where inertial factors are usually less than one, the inertial factor in the first algorithm can be taken as nonnegative numbers greater than one. The efficiency and advantage of our algorithms are illustrated by numerical experiments.

Keywords:

• Split feasibility problem
• inertial factor
• relaxed splitting method
• CQ algorithm

Disclosure statement

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

Additional information

Funding

This research is funded by The Science and Technology Development Fund, Macau SAR (File no. 0005/2019/A) and is funded by University of Macau (File no. MYRG2018-00047-FST). O Fundo para o Desenvolvimento das Ciências e da Tecnologia de Macau.