scholarly journals Strong Convergence on the Split Feasibility Problem by Mixing W -Mapping

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fugen Gao ◽  
Xiaoxiao Liu ◽  
Xiaochun Li
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, we concern with the split feasibility problem (SFP) in real Hilbert space whenever the sets involved are nonempty, closed, and convex. By mixing W -mapping with the viscosity, we introduce a new iterative algorithm for solving the split feasibility problem, and we prove that our proposed algorithm is convergent strongly to a solution of the split feasibility problem.

scholarly journals An Inertial Accelerated Algorithm for Solving Split Feasibility Problem with Multiple Output Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Huijuan Jia ◽  
Shufen Liu ◽  
Yazheng Dang
Keyword(s):  
Strong Convergence ◽  
Numerical Experiments ◽  
Convex Sets ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Matrix Inverse ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility ◽  
Self Adaptive

The paper proposes an inertial accelerated algorithm for solving split feasibility problem with multiple output sets. To improve the feasibility, the algorithm involves computing of projections onto relaxed sets (half spaces) instead of computing onto the closed convex sets, and it does not require calculating matrix inverse. To accelerate the convergence, the algorithm adopts self-adaptive rules and incorporates inertial technique. The strong convergence is shown under some suitable conditions. In addition, some newly derived results are presented for solving the split feasibility problem and split feasibility problem with multiple output sets. Finally, numerical experiments illustrate that the algorithm converges more quickly than some existing algorithms. Our results extend and improve some methods in the literature.

scholarly journals A Viscosity Approximation Method for the Split Feasibility Problems in Hilbert Space

2017 ◽  
Vol 9 (1) ◽  
pp. 84
Author(s):  
Li Yang
Keyword(s):  
Hilbert Space ◽  
Approximation Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, the most basic idea is to apply the viscosity approximation method to study the split feasibility problem (SFP), we will be in the infinite-dimensional Hilbert space to study the problem . We defined $x_{0}\in C$ as arbitrary and $x_{n+1}=(1-\alpha_{n})P_{C}(I-\lambda_{n}A^{*}(I-P_{Q})A)x_{n}+\alpha_{n}f(x_{n})$, for $n\geq0,$ where $\{\alpha_{n}\}\subset(0,1)$. Under the proper control conditions of some parameters, we show that the sequence $\{x_{n}\}$  converges strongly to a solution of SFP. The results in this paper extend and further improve the relevant conclusions in Deepho (Deepho, J. \& Kumam, P., 2015).

scholarly journals An Explicit Method for the Split Feasibility Problem with Self-Adaptive Step Sizes

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Youli Yu
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Explicit Method ◽  
The Split Feasibility Problem ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

An explicit iterative method with self-adaptive step-sizes for solving the split feasibility problem is presented. Strong convergence theorem is provided.

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