Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem
Joint Authors
Chen, Ying
Chen, Ru Dong
Guo, Yuansheng
Yu, Yanrong
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Given nonempty closed convex subsets Ci⊆Rm, i=1,2,…,t and nonempty closed convex subsets Qj⊆Rn, j=1,2,…,r, in the n- and m-dimensional Euclidean spaces, respectively.
The multiple-set split feasibility problem (MSSFP) proposed by Censor is to find a vector x∈⋂i=1tCi such that Ax∈⋂j=1rQj, where A is a given M×N real matrix.
It serves as 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.
MSSFP has a variety of specific applications in real world, such as medical care, image reconstruction, and signal processing.
In this paper, for the MSSFP, we first propose a new self-adaptive projection method by adopting Armijo-like searches, which dose not require estimating the Lipschitz constant and calculating the largest eigenvalue of the matrix ATA; besides, it makes a sufficient decrease of the objective function at each iteration.
Then we introduce a relaxed self-adaptive projection method by using projections onto half-spaces instead of those onto convex sets.
Obviously, the latter are easy to implement.
Global convergence for both methods is proved under a suitable condition.
American Psychological Association (APA)
Chen, Ying& Guo, Yuansheng& Yu, Yanrong& Chen, Ru Dong. 2012. Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-511400
Modern Language Association (MLA)
Chen, Ying…[et al.]. Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem. Abstract and Applied Analysis No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-511400
American Medical Association (AMA)
Chen, Ying& Guo, Yuansheng& Yu, Yanrong& Chen, Ru Dong. Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-511400
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-511400