scholarly journals Iterative methods for solving the multiple-sets split feasibility problem with splitting self-adaptive step size

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Yuchao Tang ◽  
Chuanxi Zhu ◽  
Hui Yu
Keyword(s):  
Iterative Methods ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

scholarly journals Self adaptive inertial relaxed $ CQ $ algorithms for solving split feasibility problem with multiple output sets

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guash Haile Taddele ◽  
Poom Kumam ◽  
Habib ur Rehman ◽  
Anteneh Getachew Gebrie
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Step Size ◽  
The Split Feasibility Problem ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

<p style='text-indent:20px;'>In this paper, we propose two new self-adaptive inertial relaxed <inline-formula><tex-math id="M2">\begin{document}$ CQ $\end{document}</tex-math></inline-formula> algorithms for solving the split feasibility problem with multiple output sets in the framework of real Hilbert spaces. The proposed algorithms involve computing projections onto half-spaces instead of onto the closed convex sets, and the advantage of the self-adaptive step size introduced in our algorithms is that it does not require the computation of operator norm. We establish and prove weak and strong convergence theorems for the iterative sequences generated by the introduced algorithms for solving the aforementioned problem. Moreover, we apply the new results to solve some other problems. Finally, we present some numerical examples to illustrate the implementation of our algorithms and compared them to some existing results.</p>

scholarly journals An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Hammed Anuoluwapo Abass ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

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.

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 On Two Projection Algorithms for the Multiple-Sets Split Feasibility Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qiao-Li Dong ◽  
Songnian He
Keyword(s):  
Adaptive Algorithm ◽  
Split Feasibility Problem ◽  
Rates Of Convergence ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Numerical Tests ◽  
Split Feasibility ◽  
Self Adaptive

We present a projection algorithm which modifies the method proposed by Censor and Elfving (1994) and also introduce a self-adaptive algorithm for the multiple-sets split feasibility problem (MSFP). The global rates of convergence are firstly investigated and the sequences generated by two algorithms are proved to converge to a solution of the MSFP. The efficiency of the proposed algorithms is illustrated by some numerical tests.

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