Circumcentering the Douglas-Rachford method

DOI10.1007/s11075-017-0399-5zbMath1395.49023arXiv1704.06737OpenAlexW2607657538MaRDI QIDQ1652791

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

Publication date: 16 July 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06737

zbMATH Keywords

linear convergenceFriedrichs anglesubspacesDouglas-Rachford methodbest approximation problemprojection and reflection operators

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Decomposition methods (49M27) Acceleration of convergence in numerical analysis (65B99)

Related Items (20)

Circumcentering approximate reflections for solving the convex feasibility problem ⋮ Circumcentering reflection methods for nonconvex feasibility problems ⋮ On the circumcentered-reflection method for the convex feasibility problem ⋮ Bregman circumcenters: basic theory ⋮ On the linear convergence of the circumcentered-reflection method ⋮ Circumcentric directions of cones ⋮ Computable centering methods for spiraling algorithms and their duals, with motivations from the theory of Lyapunov functions ⋮ The Douglas-Rachford algorithm for convex and nonconvex feasibility problems ⋮ Bregman circumcenters: monotonicity and forward weak convergence ⋮ The block-wise circumcentered-reflection method ⋮ On the centralization of the circumcentered-reflection method ⋮ Comparing the methods of alternating and simultaneous projections for two subspaces ⋮ A successive centralized circumcentered-reflection method for the convex feasibility problem ⋮ Centering projection methods for wavelet feasibility problems ⋮ 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 ⋮ SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD ⋮ Best approximation mappings in Hilbert spaces

Uses Software

• Julia
• PGFPlots
• perprof-py

Cites Work

• Unnamed Item
• Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem
• Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces
• Linear and strong convergence of algorithms involving averaged nonexpansive operators
• Recent results on Douglas-Rachford methods for combinatorial optimization problems
• The Douglas-Rachford algorithm for the case of the sphere and the line
• Error bounds for the method of alternating projections
• 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
• On the Douglas-Rachford algorithm
• Global convergence of a non-convex Douglas-Rachford iteration
• On the local convergence of the Douglas-Rachford algorithm
• Linear convergence of the Douglas–Rachford method for two closed sets
• The Douglas–Rachford Algorithm in the Absence of Convexity
• Julia: A Fresh Approach to Numerical Computing
• On Weak Convergence of the Douglas–Rachford Method
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Projection methods: an annotated bibliography of books and reviews
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
• On Projection Algorithms for Solving Convex Feasibility Problems
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• Convex analysis and monotone operator theory in Hilbert spaces
• Best approximation in inner product spaces
• Benchmarking optimization software with performance profiles.

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