On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem

2019 ◽  
Vol 84 (3) ◽  
pp. 997-1017 ◽  
Author(s):  
Suparat Kesornprom ◽  
Nattawut Pholasa ◽  
Prasit Cholamjiak
Keyword(s):  
Convergence Analysis ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

scholarly journals Regularized Methods for the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yonghong Yao ◽  
Wu Jigang ◽  
Yeong-Cheng Liou
Keyword(s):  
Signal Processing ◽  
Convergence Analysis ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Image Reconstructions ◽  
Regularized Methods ◽  
The Split Feasibility Problem ◽  
Split Feasibility

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP).

An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

2021 ◽  
pp. 2250120
Author(s):  
Yan Tang ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Banach Spaces ◽  
Split Feasibility Problem ◽  
Null Point ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Inertial Algorithm ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.

scholarly journals New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Haiying Li ◽  
Yulian Wu ◽  
Fenghui Wang
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Linear Operators ◽  
Feasibility Problem ◽  
Variable Step Size ◽  
Step Size ◽  
Bounded Linear ◽  
Variable Step ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed C Q algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.

scholarly journals Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem

2020 ◽  
Vol 25 (3) ◽  
pp. 47
Author(s):  
Guash Haile Taddele ◽  
Poom Kumam ◽  
Anteneh Getachew Gebrie ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Convex Sets ◽  
Split Feasibility Problem ◽  
Finite Family ◽  
Feasibility Problem ◽  
Extended Form ◽  
Numerical Examples ◽  
Cq Algorithm ◽  
The Split Feasibility Problem ◽  
Convergent Algorithm ◽  
Split Feasibility

In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature.

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