The iterative method for solving the proximal split feasibility problem with an application to LASSO problem

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
Xiaojun Ma ◽  
Hongwei Liu ◽  
Xiaoyin Li
Keyword(s):  
Iterative Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Lasso Problem ◽  
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 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.

scholarly journals On the Shrinking Projection Method for the Split Feasibility Problem in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Huanhuan Cui ◽  
Haixia Zhang
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Shrinking Projection Method ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, we consider the split feasibility problem in Banach spaces. By applying the shrinking projection method, we propose an iterative method for solving this problem. It is shown that the algorithm under two different choices of the stepsizes is strongly convergent to a solution of the problem.

A new iterative method for the split feasibility problem

2018 ◽  
Vol 34 (3) ◽  
pp. 313-320
Author(s):  
QIAO-LI DONG ◽  
◽  
DAN JIANG ◽  
Keyword(s):  
Inverse Problems ◽  
Linear Operator ◽  
Iterative Method ◽  
Projection Method ◽  
Numerical Experiments ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
New Iterative Method

The split feasibility problem (SFP) has many applications, which can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. In this paper, we introduce a new projection method to solve the SFP and prove its convergence under standard assumptions. Our results improve previously known corresponding methods and results of this area. The preliminary numerical experiments illustrates the advantage of our proposed methods.

Ball-relaxed projection algorithms for multiple-sets split feasibility problem

Optimization ◽  
2021 ◽  
pp. 1-31
Author(s):  
Guash Haile Taddele ◽  
Poom Kumam ◽  
Anteneh Getachew Gebrie ◽  
Jamilu Abubakar
Keyword(s):  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Split Feasibility

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.

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