The Landweber Operator Approach to the Split Equality Problem

DOI10.1137/20M1337910zbMath1461.47038OpenAlexW3130694110MaRDI QIDQ5853566

Hong-Kun Xu, Andrzej Cegielski

Publication date: 10 March 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1337910

zbMATH Keywords

nonexpansive mappingHilbert spaceprojectionlinear convergenceaveraged mappingsplit feasibilitylinear regularitysplit equalityLandweber operator

Mathematics Subject Classification ID

Convex programming (90C25) Numerical methods based on necessary conditions (49M05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (4)

A dynamic simultaneous algorithm for solving split equality fixed point problems ⋮ A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints ⋮ The split common fixed point problem with multiple output sets for strictly pseudo-contractive mappings ⋮ The split feasibility problem with multiple output sets for demicontractive mappings

Cites Work

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• Iterative methods for fixed point problems in Hilbert spaces
• A note on the split common fixed-point problem for quasi-nonexpansive operators
• Cyclic algorithms for split feasibility problems in Hilbert spaces
• Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators
• A multiprojection algorithm using Bregman projections in a product space
• General method for solving the split common fixed point problem
• Solving the split equality problem without prior knowledge of operator norms
• Landweber-type operator and its properties
• Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces
• Solving the split feasibility problem without prior knowledge of matrix norms
• The multiple-sets split feasibility problem and its applications for inverse problems
• A variable Krasnosel'skii–Mann algorithm and the multiple-set split feasibility problem
• A unified treatment of some iterative algorithms in signal processing and image reconstruction
• Iterative oblique projection onto convex sets and the split feasibility problem
• Regular Sequences of Quasi-Nonexpansive Operators and Their Applications
• Hybrid Steepest Descent Method for Variational Inequality Problem over the Fixed Point Set of Certain Quasi-nonexpansive Mappings
• On Projection Algorithms for Solving Convex Feasibility Problems
• Weak, strong and linear convergence of the CQ-method via the regularity of Landweber operators
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
• An Iteration Formula for Fredholm Integral Equations of the First Kind
• Convex analysis and monotone operator theory in Hilbert spaces
• Best approximation in inner product spaces

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