Tseng type methods for solving inclusion problems and its applications

被引:0
|
作者
Aviv Gibali
Duong Viet Thong
机构
[1] ORT Braude College,Department of Mathematics
[2] University of Haifa,The Center for Mathematics and Scientific Computation
[3] Ton Duc Thang University,Applied Analysis Research Group, Faculty of Mathematics and Statistics
来源
Calcolo | 2018年 / 55卷
关键词
Forward–backward splitting method; Viscosity approximation method; Mann-type method; Zero point; 65Y05; 65K15; 68W10; 47H06; 47H09; 47H10;
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摘要
In this paper, we introduce two modifications of the forward–backward splitting method with a new step size rule for inclusion problems in real Hilbert spaces. The modifications are based on Mann and viscosity-ideas. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish strong convergence of the proposed algorithms. We present two numerical examples, the first in infinite dimensional spaces, which illustrates mainly the strong convergence property of the algorithm. For the second example, we illustrate the performances of our scheme, compared with the classical forward–backward splitting method for the problem of recovering a sparse noisy signal. Our result extend some related works in the literature and the primary experiments might also suggest their potential applicability.
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