Paper Info
Title
Relaxed two points projection method for solving the multiple-sets split equality problem.
Abstract
The multiple-sets split equality problem, a generalization and extension of the split feasibility problem, has a variety of specific applications in real world, such as medical care, image reconstruction, and signal processing. It can be a model for many inverse problems where constraints are imposed on the solutions in the domains of two linear operators as well as in the operators’ ranges simultaneously. Although, for the split equality problem, there exist many algorithms, there are but few algorithms for the multiple-sets split equality problem. Hence, in this paper, we present a relaxed two points projection method to solve the problem; under some suitable conditions, we show the weak convergence and give a remark for the strong convergence method in the Hilbert space. The interest of our algorithm is that we transfer the problem to an optimization problem, then, based on the model, we present a modified gradient projection algorithm by selecting two different initial points in different sets for the problem (we call the algorithm as two points algorithm). During the process of iteration, we employ subgradient projections, not use the orthogonal projection, which makes the method implementable. Numerical experiments manifest the algorithm is efficient.
Year
DOI
Venue
2018
https://doi.org/10.1007/s11075-017-0375-0
Numerical Algorithms
Keywords
Field
DocType
Multiple-sets split equality problem,Relaxed two points projection method,Convergence,Hilbert space
Iterative reconstruction,Hilbert space,Weak convergence,Mathematical optimization,Subgradient method,Orthographic projection,Mathematical analysis,Projection method,Inverse problem,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
78
1
1017-1398
Citations 
PageRank 
References 
0
0.34
1
Authors
3
Name
Order
Citations
PageRank
Yazheng Dang101.35
Jian Yao293.61
Yan Gao301.01