scholarly journals Bounded perturbation resilience of a viscosity iterative method for split feasibility problems

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Iterative Method ◽  
Split Feasibility Problems ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Viscosity Iterative Method ◽  
Split Feasibility

scholarly journals Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 197
Author(s):  
Yingying Li ◽  
Yaxuan Zhang
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Lasso Problem ◽  
Bounded Perturbations ◽  
Split Feasibility

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

scholarly journals An iterative method for solving multiple-set split feasibility problems in Banach spaces

2020 ◽  
Vol 36 (1) ◽  
pp. 1-13
Author(s):  
SULIMAN AL-HOMIDAN ◽  
BASHIR ALI ◽  
YUSUF I. SULEIMAN
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Result ◽  
Uniformly Convex ◽  
Split Feasibility Problems ◽  
Uniformly Smooth ◽  
Convex Problem ◽  
Split Feasibility

"In this paper, we study generalized multiple-set split feasibility problems (in short, GMSSFP) in the frame workof p-uniformly convex real Banach spaces which are also uniformly smooth. We construct an iterative algo-rithm which is free from an operator norm and prove its strong convergence to a solution of GMSSFP, thatis, a solution of convex problem and a common fixed point of a countable family of Bregman asymptoticallyquasi-nonexpansive mappings without requirement for semi-compactness on the mappings. We illustrate ouralgorithm and convergence result by a numerical example. "

scholarly journals Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 535
Author(s):  
Yanni Guo ◽  
Xiaozhi Zhao
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Real Hilbert Space ◽  
Gradient Algorithm ◽  
Original Algorithm ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience

In this paper, a multi-parameter proximal scaled gradient algorithm with outer perturbations is presented in real Hilbert space. The strong convergence of the generated sequence is proved. The bounded perturbation resilience and the superiorized version of the original algorithm are also discussed. The validity and the comparison with the use or not of superiorization of the proposed algorithms were illustrated by solving the l 1 − l 2 problem.

scholarly journals Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jing Quan ◽  
Shih-sen Chang ◽  
Xiang Zhang
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility ◽  
Strictly Pseudononspreading Mapping

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.

Sign in / Sign up

Export Citation Format

Share Document