Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces

The split feasibility problem is to find a point x ∗ with the property that x ∗ ∈ C and A x ∗ ∈ Q , where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y , respectively, and A is a bounded linear operator from X to Y . The split feasibility problem models inverse problems a...

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Published in:	Numerical algorithms Vol. 87; no. 3; pp. 1075 - 1095
Main Authors:	Sahu, D.R., Cho, Y.J., Dong, Q.L., Kashyap, M.R., Li, X.H.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.07.2021 Springer Nature B.V
Subjects:	Algebra Algorithms Codes Computer Science Feasibility Hilbert space Inverse problems Linear operators Numeric Computing Numerical Analysis Original Paper Phase retrieval Radiation therapy Theory of Computation Weak convergence 65K05 CQ algorithm 49J52 65K10 Inertial technique Split feasibility problem Self-adaptive algorithm
ISSN:	1017-1398, 1572-9265
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Abstract	The split feasibility problem is to find a point x ∗ with the property that x ∗ ∈ C and A x ∗ ∈ Q , where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y , respectively, and A is a bounded linear operator from X to Y . The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.
AbstractList	The split feasibility problem is to find a point x ∗ with the property that x ∗ ∈ C and A x ∗ ∈ Q , where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y , respectively, and A is a bounded linear operator from X to Y . The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem. The split feasibility problem is to find a point x∗ with the property that x∗∈ C and Ax∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y, respectively, and A is a bounded linear operator from X to Y. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.
Author	Dong, Q.L. Kashyap, M.R. Li, X.H. Sahu, D.R. Cho, Y.J.
Author_xml	– sequence: 1 givenname: D.R. surname: Sahu fullname: Sahu, D.R. organization: Department of Mathematics, Institute of Science, Banaras Hindu University – sequence: 2 givenname: Y.J. surname: Cho fullname: Cho, Y.J. organization: Department of Mathematics Education, Gyeongsang National University, School of Mathematical Sciences, University of Electronic Science and Technology of China – sequence: 3 givenname: Q.L. orcidid: 0000-0001-6765-4437 surname: Dong fullname: Dong, Q.L. email: dongql@lsec.cc.ac.cn organization: Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China – sequence: 4 givenname: M.R. surname: Kashyap fullname: Kashyap, M.R. organization: Department of Mathematics, Institute of Science, Banaras Hindu University – sequence: 5 givenname: X.H. surname: Li fullname: Li, X.H. organization: Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China
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References_xml	– reference: WangFPolyak‘s gradient method for split feasibility problem constrained by level sets, NumerAlgorithms201877925938376660110.1007/s11075-017-0347-4 – reference: KesornpromSPholasaNCholamjiakPOn the convergence analysis of the gradient-CQ algorithms for the split feasibility problemNumer. Algor.2020849971017411069410.1007/s11075-019-00790-y – reference: SahuDRAnsariQHYaoJCConvergence of inexact Mann iterations generated by nearly nonexpansive sequences and applicationsNumer. Funct. Anal. Optim.20163713121338355300910.1080/01630563.2016.1206566 – reference: TibshiraniRRegression shrinkage and selection via the Lasso, J.R.Stat. Soc. Ser B19965826728813792420850.62538 – reference: AgarwalRPReganDOSahuDRFixed Point Theory for Lipschitzian-Type Mappings with Applications, Topological Fixed Point Theory and Its Applications2009New York USASpringer – reference: AnhPKVinhNTDungVTA new self-adaptive CQ algorithm with an application to the lasso problemJ. 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Snippet	The split feasibility problem is to find a point x ∗ with the property that x ∗ ∈ C and A x ∗ ∈ Q , where C and Q are nonempty closed convex subsets of real... The split feasibility problem is to find a point x∗ with the property that x∗∈ C and Ax∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert...
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SubjectTerms	Algebra Algorithms Codes Computer Science Feasibility Hilbert space Inverse problems Linear operators Numeric Computing Numerical Analysis Original Paper Phase retrieval Radiation therapy Theory of Computation
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Title	Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces
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