The block-wise circumcentered-reflection method

DOI10.1007/s10589-019-00155-0zbMath1445.90080arXiv1902.10866OpenAlexW3098426976WikidataQ126789074 ScholiaQ126789074MaRDI QIDQ2191785

Roger Behling, Luiz-Rafael Santos, José Yunier Bello Cruz

Publication date: 26 June 2020

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.10866

zbMATH Keywords

method of alternating projectionsDouglas-Rachford methodbest approximation problemaccelerating convergencecircumcenter schemelinear and finite convergence

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Decomposition methods (49M27)

Related Items (14)

On the circumcentered-reflection method for the convex feasibility problem ⋮ Bregman circumcenters: basic theory ⋮ Circumcentric directions of cones ⋮ Bregman circumcenters: monotonicity and forward weak convergence ⋮ Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization ⋮ On the centralization of the circumcentered-reflection method ⋮ A successive centralized circumcentered-reflection method for the convex feasibility problem ⋮ Unnamed Item ⋮ On the linear convergence of circumcentered isometry methods ⋮ Circumcentered methods induced by isometries ⋮ Unnamed Item ⋮ The circumcentered-reflection method achieves better rates than alternating projections ⋮ Best approximation mappings in Hilbert spaces ⋮ Infeasibility and Error Bound Imply Finite Convergence of Alternating Projections

Uses Software

• MatrixMarket
• AIR tools
• Julia

Cites Work

• Unnamed Item
• Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces
• Restricted normal cones and the method of alternating projections: theory
• Recent results on Douglas-Rachford methods for combinatorial optimization problems
• A randomized Kaczmarz algorithm with exponential convergence
• On the convergence of von Neumann's alternating projection algorithm for two sets
• Circumcentering the Douglas-Rachford method
• The Douglas-Rachford algorithm for convex and nonconvex feasibility problems
• A cyclic Douglas-Rachford iteration scheme
• The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
• AIR tools II: algebraic iterative reconstruction methods, improved implementation
• On the linear convergence of the circumcentered-reflection method
• Fundamentals of Computerized Tomography
• The Douglas--Rachford Algorithm for Two (Not Necessarily Intersecting) Affine Subspaces
• Julia: A Fresh Approach to Numerical Computing
• Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit
• Accelerating the convergence of the method of alternating projections
• Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
• On Projection Algorithms for Solving Convex Feasibility Problems
• On circumcenters of finite sets in Hilbert spaces
• On circumcenter mappings induced by nonexpansive operators
• The Cyclic Douglas-Rachford Method for Inconsistent Feasibility Problems
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• Best approximation in inner product spaces

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