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 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.

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 Regularized Methods for the Split Feasibility Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yonghong Yao ◽  
Wu Jigang ◽  
Yeong-Cheng Liou
Keyword(s):  
Signal Processing ◽  
Convergence Analysis ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Image Reconstructions ◽  
Regularized Methods ◽  
The Split Feasibility Problem ◽  
Split Feasibility

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP).

scholarly journals The Split Feasibility Problem and Its Solution Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Biao Qu ◽  
Binghua Liu
Keyword(s):  
Signal Processing ◽  
Real World ◽  
Lipschitz Constant ◽  
Split Feasibility Problem ◽  
Solution Algorithm ◽  
Feasibility Problem ◽  
Step Size ◽  
Convergence Results ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and two previous iterations to get the next iteration, and its step size can be calculated directly. It not only improves the flexibility of the algorithm, but also avoids computing the largest eigenvalue of the related matrix or estimating the Lipschitz constant in each iteration. Theoretical convergence results are established under some suitable conditions.

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.

Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chibueze C. Okeke ◽  
Lateef O. Jolaoso ◽  
Yekini Shehu
Keyword(s):  
Strong Convergence ◽  
Prior Knowledge ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Convergence Results ◽  
Split Feasibility

Abstract In this paper, we propose two inertial accelerated algorithms which do not require prior knowledge of operator norm for solving split feasibility problem with multiple output sets in real Hilbert spaces. We prove weak and strong convergence results for approximating the solution of the considered problem under certain mild conditions. We also give some numerical examples to demonstrate the performance and efficiency of our proposed algorithms over some existing related algorithms in the literature.

scholarly journals A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 789 ◽  
Author(s):  
Suthep Suantai ◽  
Suparat Kesornprom ◽  
Prasit Cholamjiak
Keyword(s):  
Compressed Sensing ◽  
Line Search ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Cq Algorithm ◽  
Line Search Techniques ◽  
Weak Convergence Theorem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper, we focus on studying the split feasibility problem (SFP), which has many applications in signal processing and image reconstruction. A popular technique is to employ the iterative method which is so called the relaxed CQ algorithm. However, the speed of convergence usually depends on the way of selecting the step size of such algorithms. We aim to suggest a new hybrid CQ algorithm for the SFP by using the self adaptive and the line-search techniques. There is no computation on the inverse and the spectral radius of a matrix. We then prove the weak convergence theorem under mild conditions. Numerical experiments are included to illustrate its performance in compressed sensing. Some comparisons are also given to show the efficiency with other CQ methods in the literature.

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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