Abstract
In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.
Highlights
Censor and Elfving [12] introduced the following Split Convex Feasibility Problem (SCFP), see [11], find x ∈ C such that Ax ∈ Q, (1)where A : Rk → Rm is a bounded and linear operator, C ⊆ Rk and Q ⊆ Rm are nonempty, closed and convex sets
The SCFP was introduced in Euclidean spaces, and afterwards extended to infinite dimensional spaces as well as applied successfully in the field of intensitymodulated radiation therapy (IMRT) treatment planning, see [11,12,13,15]
Motivated by the above works, we propose a new relaxed CQ method with alternated inertial procedure for solving SCFPs
Summary
Censor and Elfving [12] introduced the following Split Convex Feasibility Problem (SCFP), see [11], find x ∈ C such that Ax ∈ Q,. Where θn ∈ [0, 1) is an inertial factor and λn is a positive sequence It was shown via numerical experiments in the field of image reconstruction, that (4) and other associated methods, such as [1,2,6,7,8,18,21,31,32,34], have greatly improved the performance of their non-inertial algorithms, that is, when θn = 0. This idea is referred to as inertial algorithms In this spirit, several inertial-type methods for solving SCFPs have been proposed recently, see [16,44,45,46,47,51], just to name a few.
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