Hybrid CQ projection algorithm with line-search process for the split feasibility problem

This paper deals with the split feasibility problem that requires to find a point closest to a closed convex set in one space such that its image under a linear transformation will be closest to another closed convex set in the image space. By combining perturbed strategy with inertial technique, we construct an inertial perturbed projection algorithm for solving the split feasibility problem. Under some suitable conditions, we show the asymptotic convergence. The results improve and extend the algorithms presented in Byrne (2002) and in Zhao and Yang (2005) and the related convergence theorem.

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

Mathematics ◽

10.3390/math7090789 ◽

2019 ◽

Vol 7 (9) ◽

pp. 789 ◽

Cited By ~ 3

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.

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An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

Asian-European Journal of Mathematics ◽

10.1142/s1793557122501200 ◽

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.

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Approximating common fixed points of averaged self-mappings with applications to the split feasibility problem and maximal monotone operators in Hilbert spaces

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2013-190 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 4

Author(s):

Young-Ye Huang ◽

Chung-Chien Hong

Keyword(s):

Fixed Points ◽

Hilbert Spaces ◽

Maximal Monotone ◽

Maximal Monotone Operators ◽

Split Feasibility Problem ◽

Monotone Operators ◽

Common Fixed Points ◽

Feasibility Problem ◽

The Split Feasibility Problem ◽

Split Feasibility

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The Split Feasibility Problem

Applied Iterative Methods ◽

10.1201/b10651-27 ◽

2007 ◽

pp. 215-220

Keyword(s):

Split Feasibility Problem ◽

Feasibility Problem ◽

The Split Feasibility Problem ◽

Split Feasibility

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New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces

Journal of Mathematics ◽

10.1155/2021/6624509 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Haiying Li ◽

Yulian Wu ◽

Fenghui Wang

Keyword(s):

Hilbert Spaces ◽

Split Feasibility Problem ◽

Linear Operators ◽

Feasibility Problem ◽

Variable Step Size ◽

Step Size ◽

Bounded Linear ◽

Variable Step ◽

The Split Feasibility Problem ◽

Split Feasibility

The split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed C Q algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.

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