New inertial relaxed method for solving split feasibilities
Yekini Shehu,Aviv Gibali +1 more
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TLDR
A relaxed CQ method with alternated inertial step for solving split feasibility problems and convergence of the sequence generated by the method under some suitable assumptions is given.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.read more
Citations
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Journal ArticleDOI
Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces
TL;DR: A new inertial relaxed CQ algorithm is introduced for solving the split feasibility problem in real Hilbert spaces and weak convergence of the proposed CQ algorithms under certain mild conditions is established.
Journal ArticleDOI
Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications
TL;DR: In this paper, four self-adaptive iterative iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces, and strong convergence theorems of these algorithms are established under mild and standard assumptions.
Journal ArticleDOI
Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems
Bing Tan,Liya Liu,Xiaolong Qin +2 more
TL;DR: Two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces are introduced and strong convergence theorems of the suggested algorithms are obtained under suitable conditions.
Journal ArticleDOI
Global and linear convergence of alternated inertial methods for split feasibility problems
TL;DR: This paper obtains global convergence of the sequences of iterates generated by the proposed methods under some appropriate conditions and shows that these sequences converge linearly when the split feasibility problem satisfies some bounded linear regularity property.
References
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
TL;DR: This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space, and a concise exposition of related constructive fixed point theory that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, and convex feasibility.
Journal ArticleDOI
Some methods of speeding up the convergence of iteration methods
TL;DR: In this article, the authors consider the problem of minimizing the differentiable functional (x) in Hilbert space, so long as this problem reduces to the solution of the equation grad(x) = 0.