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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00999-2