A unified treatment of some perturbed fixed point iterative methods with an infinite pool of operators

DOI10.1088/1361-6420/33/4/044002zbMath1394.47069OpenAlexW2594107622MaRDI QIDQ5346621

Mokhtar Abbasi, Touraj Nikazad

Publication date: 26 May 2017

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6420/33/4/044002

zbMATH Keywords

fixed pointprojection methodconvergence theoremquasi-nonexpansive operatorconvex feasibilitycutter operatorparacontracting operatorsuperiorization methodologyperturbation-resilient iterative method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Iterative numerical methods for linear systems (65F10)

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Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm ⋮ Numerical investigation of Fredholm integral equation of the first kind with noisy data ⋮ A new step size rule for the superiorization method and its application in computerized tomography ⋮ Bounded perturbations resilient iterative methods for linear systems and least squares problems: operator-based approaches, analysis, and performance evaluation ⋮ String-averaging algorithms for convex feasibility with infinitely many sets ⋮ Column-oriented algebraic iterative methods for nonnegative constrained least squares problems ⋮ String-averaging incremental stochastic subgradient algorithms

Cites Work

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• Extrapolation and local acceleration of an iterative process for common fixed point problems
• Zero-convex functions, perturbation resilience, and subgradient projections for feasibility-seeking methods
• Block-iterative methods for consistent and inconsistent linear equations
• Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
• A parallel subgradient projections method for the convex feasibility problem
• Iterative algorithms for large partitioned linear systems, with applications to image reconstruction
• Convergence of sequential and asynchronous nonlinear paracontractions
• Block-iterative projection methods for parallel computation of solutions to convex feasibility problems
• An acceleration scheme for cyclic subgradient projections method
• Convergence and perturbation resilience of dynamic string-averaging projection methods
• Strict Fejér monotonicity by superiorization of feasibility-seeking projection methods
• Extrapolation algorithm for affine-convex feasibility problems
• Convergence of string-averaging method for a class of operators
• Impulse Control of Multidimensional Jump Diffusions in Finite Time Horizon
• Perturbation-Resilient Iterative Methods with an Infinite Pool of Mappings
• Stable Convergence Theorems for Infinite Products and Powers of Nonexpansive Mappings
• Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections
• Incremental Subgradients for Constrained Convex Optimization: A Unified Framework and New Methods
• On Diagonally Relaxed Orthogonal Projection Methods
• Cyclic subgradient projections
• An Optimal Control Theory for Discrete Event Systems
• Convergence of String-Averaging Projection Schemes for Inconsistent Convex Feasibility Problems
• Optimal Supervisory Control of Discrete Event Dynamical Systems
• On Projection Algorithms for Solving Convex Feasibility Problems
• Block-Iterative Algorithms with Diagonally Scaled Oblique Projections for the Linear Feasibility Problem
• Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces

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