Douglas–Rachford Splitting Method with Linearization for the Split Feasibility Problem

Abstract

The aim of this article is to introduce the Douglas–Rachford splitting method with linearization to solve the split feasibility problem (SFP). Our proposed method includes two existing methods in work of Tang et al. and Wang as special cases. The ranges of the parameters in work of Tang et al. are extended from (0,1) to (0,2). Under standard conditions, we prove the weak convergence of proposed algorithms. We also provide two numerical experiments to illustrate the effectiveness of the proposed algorithm by comparing the algorithms in work of Tang et al. and Wang.

Keywords

• split feasibility problem
• Douglas–Rachford splitting method with linearization
• relaxed Douglas–Rachford splitting method with linearization
• CQ algorithm