Journal ArticleDOI
Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method
Yekini Shehu,Olaniyi S. Iyiola +1 more
TLDR
In this article, a proximal split feasibility algorithm with an additional inertial extrapolation term was proposed for solving the proximal-split feasibility problem under weaker conditions on the step sizes, where the convex and lower semi continuous objective functions are assumed to be non-smooth.Abstract:
In this paper, we present a proximal split feasibility algorithm with an additional inertial extrapolation term for solving a proximal split feasibility problem under weaker conditions on the step sizes. The two convex and lower semi continuous objective functions are assumed to be non-smooth. Some applications to split inclusion problem and split equilibrium problem are given. We demonstrate the efficiency of the proposed algorithm with numerical experiments.read more
Citations
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Journal ArticleDOI
New inertial relaxed method for solving split feasibilities
Yekini Shehu,Aviv Gibali +1 more
TL;DR: 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.
Journal ArticleDOI
A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications
Aviv Gibali,Dang Thi Mai +1 more
TL;DR: In this article, an inertial relaxation of the CQ algorithm for solving split feasibility problems (SFP) in real Hilbert spaces is proposed and shown to achieve weak convergence under mild and standard conditions.
Journal ArticleDOI
Inertial Extragradient Algorithms for Solving Equilibrium Problems
TL;DR: Two new algorithms based upon the extragradient and inertial methods for solving pseudomonotone equilibrium problems in real Hilbert spaces are introduced and numerical results show that they are more efficient than some existing methods for equilibrium problems.
Journal ArticleDOI
Modified Tseng’s extragradient algorithms for variational inequality problems
Duong Viet Thong,Dang Van Hieu +1 more
TL;DR: In this article, two modified Tseng's extragradient methods using the inertial technique were introduced to solve the monotone variational inequality problems in the framework of real Hilbert spaces.
Journal ArticleDOI
New self-adaptive step size algorithms for solving split variational inclusion problems and its applications
Yan Tang,Aviv Gibali +1 more
TL;DR: Three simple iterative methods for solving the split variational inclusion problem (SVIP) are introduced and weak and strong convergence theorems are established under mild and standard assumptions.
References
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Journal ArticleDOI
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.
Journal ArticleDOI
Monotone Operators and the Proximal Point Algorithm
TL;DR: In this paper, the proximal point algorithm in exact form is investigated in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by an arbitrary maximal monotone operator T.
Journal ArticleDOI
Signal recovery by proximal forward-backward splitting ∗
TL;DR: It is shown that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties, which makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems.
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