scholarly journals Alternating iterative algorithms for the split equality problem without prior knowledge of operator norms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hai Yu ◽  
Fenghui Wang
Keyword(s):  
Prior Knowledge ◽  
Iterative Algorithms ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Operator Norms

Solving the split equality problem without prior knowledge of operator norms

Optimization ◽  
2014 ◽  
Vol 64 (9) ◽  
pp. 1887-1906 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Jing Zhao
Keyword(s):  
Prior Knowledge ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Operator Norms

scholarly journals Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Wenchao Wang
Keyword(s):  
Fixed Point ◽  
Iterative Algorithms ◽  
Nonlinear Problems ◽  
Fixed Point Problem ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Point Problem ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Internal Perturbation

In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

scholarly journals Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 928 ◽  
Author(s):  
Dianlu Tian ◽  
Lining Jiang ◽  
Luoyi Shi
Keyword(s):  
Inverse Problem ◽  
Gradient Methods ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Split Equality Problem ◽  
Selection Technique ◽  
Equality Problem

The inverse problem is one of the four major problems in computational mathematics. There is an inverse problem in medical image reconstruction and radiotherapy that is called the multiple-sets split equality problem. The multiple-sets split equality problem is a unified form of the split feasibility problem, split equality problem, and split common fixed point problem. In this paper, we present two iterative algorithms for solving it. The suggested algorithms are based on the gradient method with a selection technique. Based on this technique, we only need to calculate one projection in each iteration.

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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