Modified projection methods for the split feasibility problem and the multiple-sets split feasibility problem

2012 ◽  
Vol 219 (4) ◽  
pp. 1644-1653 ◽  
Author(s):  
Jinling Zhao ◽  
Yanjun Zhang ◽  
Qingzhi Yang
Keyword(s):  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

scholarly journals Modified Halfspace-Relaxation Projection Methods for Solving the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Min Li
Keyword(s):  
Lower Bounds ◽  
Split Feasibility Problem ◽  
Step Length ◽  
Projection Methods ◽  
Numerical Results ◽  
Feasibility Problem ◽  
New Methods ◽  
Hrp Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility

This paper presents modified halfspace-relaxation projection (HRP) methods for solving the split feasibility problem (SFP). Incorporating with the techniques of identifying the optimal step length with positive lower bounds, the new methods improve the efficiencies of the HRP method (Qu and Xiu (2008)). Some numerical results are reported to verify the computational preference.

scholarly journals The Split Feasibility Problem with Some Projection Methods in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Toshiharu Kawasaki ◽  
Hiroko Manaka
Keyword(s):  
Banach Spaces ◽  
Metric Projection ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Equivalent Equation ◽  
The Split Feasibility Problem ◽  
Sunny Generalized Nonexpansive Retraction ◽  
Split Feasibility ◽  
Mathematical Programing

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

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 S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

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