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.

A halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3211-3227 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
Relatively Nonexpansive ◽  
The Split Feasibility Problem ◽  
Split Feasibility

We study the split feasibility problem (SFP) involving the fixed point problems (FPP) in the framework of p-uniformly convex and uniformly smooth Banach spaces. We propose a Halpern-type iterative scheme for solving the solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then we prove its strong convergence theorem of the sequences generated by our iterative scheme under implemented conditions. We finally provide some numerical examples and demonstrate the efficiency of the proposed algorithm. The obtained result of this paper complements many recent results in this direction.

scholarly journals An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Huijuan Jia ◽  
Shufen Liu ◽  
Yazheng Dang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Maximal Monotone ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Mild Assumption ◽  
Inertial Technique ◽  
Split Feasibility

In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of A T A. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.

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 Perturbed Projection Algorithm with Inertial Technique for Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yazheng Dang ◽  
Yan Gao ◽  
Yanli Han
Keyword(s):  
Convergence Theorem ◽  
Convex Set ◽  
Split Feasibility Problem ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Asymptotic Convergence ◽  
Closed Convex Set ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility

This paper deals with the split feasibility problem that requires to find a point closest to a closed convex set in one space such that its image under a linear transformation will be closest to another closed convex set in the image space. By combining perturbed strategy with inertial technique, we construct an inertial perturbed projection algorithm for solving the split feasibility problem. Under some suitable conditions, we show the asymptotic convergence. The results improve and extend the algorithms presented in Byrne (2002) and in Zhao and Yang (2005) and the related convergence theorem.

scholarly journals Convergence Theorem of Two Sequences for Solving the Modified Generalized System of Variational Inequalities and Numerical Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 916
Author(s):  
Anchalee Sripattanet ◽  
Atid Kangtunyakarn
Keyword(s):  
Variational Inequalities ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
System Of Variational Inequalities ◽  
Generalized System ◽  
Constrained Convex Minimization Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The purpose of this paper is to introduce an iterative algorithm of two sequences which depend on each other by using the intermixed method. Then, we prove a strong convergence theorem for solving fixed-point problems of nonlinear mappings and we treat two variational inequality problems which form an approximate modified generalized system of variational inequalities (MGSV). By using our main theorem, we obtain the additional results involving the split feasibility problem and the constrained convex minimization problem. In support of our main result, a numerical example is also presented.

Sign in / Sign up

Export Citation Format

Share Document