Iterative algorithms for the multiple-sets split feasibility problem in Hilbert spaces

In this paper, for the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a linear bounded mapping will be closest to another family of closed convex subsets in the image space, we study several iterati...

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Bibliographic Details
Published inNumerical algorithms Vol. 76; no. 3; pp. 783 - 798
Main Author Buong, Nguyen
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2017
Springer Nature B.V
Subjects
Algebra
Algorithms
Codes
Computer Science
Feasibility
Hilbert space
Iterative algorithms
Iterative methods
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
47H09
47J05
Variational inequality
49J30
Nonexpansive mapping
Fixed point
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Summary:In this paper, for the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a linear bounded mapping will be closest to another family of closed convex subsets in the image space, we study several iterative methods for finding a solution, which solves a certain variational inequality. We show that particular cases of our algorithms are some improvements for existing ones in literature. We also give two numerical examples for illustrating our algorithms.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0282-4