scholarly journals An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Luoyi Shi ◽  
Ru Dong Chen ◽  
Yu Jing Wu
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Linear Operators ◽  
Feasibility Problem ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Infinite Dimensional ◽  
Equality Problem ◽  
Split Feasibility

The multiple-sets split equality problem (MSSEP) requires finding a pointx∈∩i=1NCi,y∈∩j=1MQjsuch thatAx=By, whereNandMare positive integers,{C1,C2,…,CN}and{Q1,Q2,…,QM}are closed convex subsets of Hilbert spacesH1,H2, respectively, andA:H1→H3,B:H2→H3are two bounded linear operators. WhenN=M=1, the MSSEP is called the split equality problem (SEP). If  B=I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.

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 A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces

2015 ◽  
Vol 31 (3) ◽  
pp. 349-357
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
MUJAHID ABBAS ◽  
YEKINI SHEHU ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Contractive Mapping ◽  
Convergence Result ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility ◽  
General Convergence

We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces.

scholarly journals General Split Feasibility Problems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Eslamian ◽  
Abdul Latif
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility

Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

scholarly journals A Strongly Convergent Method for the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Naseer Shahzad
Keyword(s):  
Hilbert Spaces ◽  
Extragradient Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Convergence Point ◽  
Convergent Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
Regularized Method

The purpose of this paper is to introduce and analyze a strongly convergent method which combined regularized method, with extragradient method for solving the split feasibility problem in the setting of infinite-dimensional Hilbert spaces. Note that the strong convergence point is the minimum norm solution of the split feasibility problem.

scholarly journals Linear Convergence of an Iterative Algorithm for Solving the Multiple-Sets Split Feasibility Problem

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 644 ◽  
Author(s):  
Tingting Tian ◽  
Luoyi Shi ◽  
Rudong Chen
Keyword(s):  
Iterative Algorithm ◽  
Orthogonal Projection ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Split Feasibility Problem ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Step Size ◽  
Bounded Linear ◽  
Split Feasibility

In this paper, we propose the simultaneous sub-gradient projection algorithm with the dynamic step size (SSPA for short) for solving the multiple-sets split feasibility problem (MSSFP for short) and investigate its linear convergence. We involve a notion of bounded linear regularity for the MSSFP and construct several sufficient conditions to prove the linear convergence for the SSPA. In particular, the SSPA is an easily calculated algorithm that uses orthogonal projection onto half-spaces. Furthermore, some numerical results are provided to verify the effectiveness of our proposed algorithm.

scholarly journals A Modified Halpern's Iterative Scheme for Solving Split Feasibility Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Jitsupa Deepho ◽  
Poom Kumam
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The purpose of this paper is to introduce and study a modified Halpern’s iterative scheme for solving the split feasibility problem (SFP) in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu (Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018) and some others.

scholarly journals Split equality fixed point problems for asymptotically quasi-pseudocontractive operators

2020 ◽  
Vol 36 (1) ◽  
pp. 147-157
Author(s):  
XIAOLI FANG ◽  
TAE-HWA KIM ◽  
YAQIN WANG
Keyword(s):  
Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Split Equality Problem ◽  
Special Cases ◽  
Equality Problem ◽  
Split Feasibility

In this paper, we consider a split equality fixed point problem for asymptotically quasi-pseudo contractive operators which includes split feasibility problem, split equality problem, split fixed point problem etc, as special cases. Furthermore we propose a new algorithm for solving the split equality fixed point problem, and prove a weak and strong convergence theorem. The results obtained in this paper generalize and improve the recent ones announced by many others.

scholarly journals A New Extragradient-Type Algorithm for the Split Feasibility Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Yazheng Dang ◽  
Yan Gao ◽  
Bo Wang
Keyword(s):  
Hilbert Spaces ◽  
Extragradient Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Subgradient Extragradient Method ◽  
Type Method ◽  
Infinite Dimensional ◽  
Type Algorithm ◽  
The Split Feasibility Problem ◽  
Split Feasibility

We consider the split feasibility problem (SFP) in Hilbert spaces, inspired by extragradient method presented by Ceng, Ansari for split feasibility problem, subgradient extragradient method proposed by Censor, and variant extragradient-type method presented by Yao for variational inequalities; we suggest an extragradient-type algorithm for the SFP. We prove the strong convergence under some suitable conditions in infinite-dimensional Hilbert spaces.

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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