scholarly journals A Regularized Algorithm for the Proximal Split Feasibility Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhangsong Yao ◽  
Sun Young Cho ◽  
Shin Min Kang ◽  
Li-Jun Zhu
Keyword(s):  
Strong Convergence ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Split Feasibility ◽  
Regularized Method

The proximal split feasibility problem has been studied. A regularized method has been presented for solving the proximal split feasibility problem. Strong convergence theorem is given.

scholarly journals An intermixed iteration for constrained convex minimization problem and split feasibility problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kanyanee Saechou ◽  
Atid Kangtunyakarn
Keyword(s):  
Strong Convergence ◽  
Minimization Problem ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization Problem ◽  
Split Feasibility

Abstract In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.

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 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.

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.

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.

scholarly journals Solving a Split Feasibility Problem by the Strong Convergence of Two Projection Algorithms in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Yaé Ulrich Gaba
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Convex Feasibility ◽  
Split Feasibility

The goal of this manuscript is to establish strong convergence theorems for inertial shrinking projection and CQ algorithms to solve a split convex feasibility problem in real Hilbert spaces. Finally, numerical examples were obtained to discuss the performance and effectiveness of our algorithms and compare the proposed algorithms with the previous shrinking projection, hybrid projection, and inertial forward-backward methods.

scholarly journals WEAK AND STRONG CONVERGENCE THEOREMS OF ALGORITHMIC SCHEMES FOR THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM

2021 ◽  
Vol 226 (15) ◽  
pp. 28-35
Author(s):  
Nguyễn Bường ◽  
Nguyễn Dương Nguyễn
Keyword(s):  
Strong Convergence ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Split Feasibility

Trong bài báo này, để giải bài toán chấp nhận tách đa tập (MSSFP) trong không gian Hilbert, chúng tôi trình bày một cách tiếp cận tổng quát để xây dựng các phương pháp lặp. Chúng tôi đề xuất một lược đồ thuật toán xâu trung bình với sự hội tụ yếu và một lược đồ thuật toán xâu trung bình với sự hội tụ mạnh. Lược đồ thuật toán xâu trung bình với sự hội tụ mạnh được xây dựng dựa trên phương pháp lặp tổng quát cho ánh xạ không giãn, trong đó cỡ bước được tính toán trực tiếp trong mỗi bước lặp mà không cần sử dụng chuẩn của toán tử. Những lược đồ thuật toán này không chỉ bao hàm những cải tiến của phương pháp lặp vòng và lặp đồng thời đã biết như những trường hợp riêng mà còn bao hàm cả những phương pháp lặp mới

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