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).

scholarly journals A Note on Approximating Curve with 1-Norm Regularization Method for the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Songnian He ◽  
Wenlong Zhu
Keyword(s):  
Regularization Method ◽  
Split Feasibility Problem ◽  
Solution Set ◽  
Feasibility Problem ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
The Split Feasibility Problem ◽  
The Relationship ◽  
Split Feasibility

Inspired by the very recent results of Wang and Xu (2010), we study properties of the approximating curve with 1-norm regularization method for the split feasibility problem (SFP). The concept of the minimum-norm solution set of SFP in the sense of 1-norm is proposed, and the relationship between the approximating curve and the minimum-norm solution set is obtained.

scholarly journals The Split Feasibility Problem and Its Solution Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Biao Qu ◽  
Binghua Liu
Keyword(s):  
Signal Processing ◽  
Real World ◽  
Lipschitz Constant ◽  
Split Feasibility Problem ◽  
Solution Algorithm ◽  
Feasibility Problem ◽  
Step Size ◽  
Convergence Results ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and two previous iterations to get the next iteration, and its step size can be calculated directly. It not only improves the flexibility of the algorithm, but also avoids computing the largest eigenvalue of the related matrix or estimating the Lipschitz constant in each iteration. Theoretical convergence results are established under some suitable conditions.

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.

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