Iterative methods for solving the multiple-sets split feasibility problem with splitting self-adaptive step size

Fixexd point theory and applications

Chuanxi Zhu¹  Yuchao Tang¹  Hui Yu² 

[1] Department of Mathematics, Nanchang University, Nanchang, P.R. China;School of Information Engineering, Nanchang University, Nanchang, P.R. China

关键词: multiple-sets split feasibility problem;    self-adaptive step size;    compressive sensing;    lasso problem;    90C25;    90C30;    47J25;   

DOI  :  10.1186/s13663-015-0430-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce an iterative algorithm for solving the multiple-sets split feasibility problem with splitting self-adaptive step size. This step size is calculated directly from the iteration process without need to know the spectral norm of linear operators. We also generalize the chosen step size to a relaxed iterative algorithm. Theoretical convergence is proved in an infinite dimensional Hilbert space. Some numerical experiments are presented to verify the effectiveness of our proposed methods.

【 授权许可】

CC BY