scholarly journals On global convergence rate of two acceleration projection algorithms for solving the multiple-sets split feasibility problem

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3243-3252 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Yanmin Zhao
Keyword(s):  
Global Convergence ◽  
Convergence Rate ◽  
Numerical Experiments ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Split Feasibility ◽  
Global Convergence Rate

In this paper, we introduce two fast projection algorithms for solving the multiple-sets split feasibility problem (MSFP). Our algorithms accelerate algorithms proposed in [8] and are proved to have a global convergence rate O(1=n2). Preliminary numerical experiments show that these algorithms are practical and promising.

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 On Two Projection Algorithms for the Multiple-Sets Split Feasibility Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qiao-Li Dong ◽  
Songnian He
Keyword(s):  
Adaptive Algorithm ◽  
Split Feasibility Problem ◽  
Rates Of Convergence ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Numerical Tests ◽  
Split Feasibility ◽  
Self Adaptive

We present a projection algorithm which modifies the method proposed by Censor and Elfving (1994) and also introduce a self-adaptive algorithm for the multiple-sets split feasibility problem (MSFP). The global rates of convergence are firstly investigated and the sequences generated by two algorithms are proved to converge to a solution of the MSFP. The efficiency of the proposed algorithms is illustrated by some numerical tests.

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 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 The inertial relaxed algorithm with Armijo-type line search for solving multiple-sets split feasibility problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenting Chen ◽  
Meixia Li
Keyword(s):  
Signal Processing ◽  
Numerical Experiments ◽  
Line Search ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Sparse Signal ◽  
Mild Conditions ◽  
Sparse Signal Processing ◽  
Fuzzy Image ◽  
Split Feasibility

AbstractThe multiple-sets split feasibility problem is the generalization of split feasibility problem, which has been widely used in fuzzy image reconstruction and sparse signal processing systems. In this paper, we present an inertial relaxed algorithm to solve the multiple-sets split feasibility problem by using an alternating inertial step. The advantage of this algorithm is that the choice of stepsize is determined by Armijo-type line search, which avoids calculating the norms of operators. The weak convergence of the sequence obtained by our algorithm is proved under mild conditions. In addition, the numerical experiments are given to verify the convergence and validity of the algorithm.

scholarly journals An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yazheng Dang ◽  
Yan Gao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Convex Sets ◽  
Lipschitz Constant ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Fixed Constant ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The multiple-set split feasibility problem (MSSFP), as a generalization of the split feasibility problem, is to find a point in the intersection of a family of closed convex sets in one space such that its image under a linear transformation will be in the intersection of another family of closed convex sets in the image space. Censor et al. (2005) proposed a method for solving the multiple-set split feasibility problem (MSSFP), whose efficiency depends heavily on the step size, a fixed constant related to the Lipschitz constant of∇p(x)which may be slow. In this paper, we present an accelerated algorithm by introducing an extrapolated factor to solve the multiple-set split feasibility problem. The framework encompasses the algorithm presented by Censor et al. (2005). The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation.

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.

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