SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD
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Publication:4992365
DOI10.1017/S1446788719000570zbMath1477.46078arXiv1809.07181OpenAlexW3008561645MaRDI QIDQ4992365
Scott B. Lindstrom, Brailey Sims
Publication date: 8 June 2021
Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.07181
Set-valued and variational analysis (49J53) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) History of calculus of variations and optimal control (49-03) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02) Numerical methods in optimal control (49M99)
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Uses Software
Cites Work
- On the order of the operators in the Douglas-Rachford algorithm
- Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem
- On Slater's condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces
- Inertial Douglas-Rachford splitting for monotone inclusion problems
- Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces
- Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
- Linear and strong convergence of algorithms involving averaged nonexpansive operators
- Iterative methods for fixed point problems in Hilbert spaces
- Attouch-Théra duality revisited: Paramonotonicity and operator splitting
- Recent results on Douglas-Rachford methods for combinatorial optimization problems
- Partial inverse of a monotone operator
- Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
- A Lyapunov-type approach to convergence of the Douglas-Rachford algorithm for a nonconvex setting
- A new projection method for finding the closest point in the intersection of convex sets
- The Douglas-Rachford algorithm for the case of the sphere and the line
- On the convergence rate of Douglas-Rachford operator splitting method
- Convex analysis and nonlinear optimization. Theory and examples.
- Local linear convergence for alternating and averaged nonconvex projections
- Removing multiplicative noise by Douglas-Rachford splitting methods
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Circumcentering the Douglas-Rachford method
- Solving graph coloring problems with the Douglas-Rachford algorithm
- Dynamics of the Douglas-Rachford method for ellipses and \(p\)-spheres
- Matrix product constraints by projection methods
- Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm
- Tight global linear convergence rate bounds for Douglas-Rachford splitting
- About intrinsic transversality of pairs of sets
- A feasibility approach for constructing combinatorial designs of circulant type
- The Douglas-Rachford algorithm in the affine-convex case
- An alternating projection that does not converge in norm
- The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
- An enhanced formulation for solving graph coloring problems with the Douglas-Rachford algorithm
- 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
- Douglas-Rachford splitting for the sum of a Lipschitz continuous and a strongly monotone operator
- On the asymptotic behaviour of the Aragón Artacho-Campoy algorithm
- On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers
- On the Douglas-Rachford algorithm
- On Douglas-Rachford operators that fail to be proximal mappings
- On the linear convergence of the circumcentered-reflection method
- Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm
- The Douglas-Rachford algorithm for a hyperplane and a doubleton
- Global convergence of a non-convex Douglas-Rachford iteration
- A family of projective splitting methods for the sum of two maximal monotone operators
- About regularity of collections of sets
- On the local convergence of the Douglas-Rachford algorithm
- On Fej\'er monotone sequences and nonexpansive mappings
- New Douglas--Rachford Algorithmic Structures and Their Convergence Analyses
- Linear convergence of the Douglas–Rachford method for two closed sets
- The Douglas--Rachford Algorithm for Two (Not Necessarily Intersecting) Affine Subspaces
- Stadium Norm and Douglas-Rachford Splitting: A New Approach to Road Design Optimization
- Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study
- Splitting Methods in Communication, Imaging, Science, and Engineering
- The Douglas–Rachford Algorithm in the Absence of Convexity
- Proximal Splitting Methods in Signal Processing
- On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
- DOUGLAS–RACHFORD FEASIBILITY METHODS FOR MATRIX COMPLETION PROBLEMS
- Convergence Rate Analysis for Averaged Fixed Point Iterations in Common Fixed Point Problems
- Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
- On Weak Convergence of the Douglas–Rachford Method
- APPLICATION OF PROJECTION ALGORITHMS TO DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS
- The Split Bregman Method for L1-Regularized Problems
- ITERATIVE PROJECTION AND REFLECTION METHODS: THEORY AND PRACTICE
- On the Range of the Douglas–Rachford Operator
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples
- Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit
- General Projective Splitting Methods for Sums of Maximal Monotone Operators
- Decomposition through formalization in a product space
- A relaxed projection method for variational inequalities
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Monotone Operators and the Proximal Point Algorithm
- Reflection Methods for Inverse Problems with Applications to Protein Conformation Determination
- The Complexity of Bit Retrieval
- Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
- Finding maximum rank moment matrices by facial reduction on primal form and Douglas-Rachford iteration
- A new proximal point iteration that converges weakly but not in norm
- Solving monotone inclusions via compositions of nonexpansive averaged operators
- On Projection Algorithms for Solving Convex Feasibility Problems
- Norm convergence of realistic projection and reflection methods
- A weakly convergent fully inexact Douglas-Rachford method with relative error tolerance
- Ergodic behaviour of a Douglas-Rachford operator away from the origin
- Douglas--Rachford Splitting and ADMM for Nonconvex Optimization: Tight Convergence Results
- Linear Convergence of Projection Algorithms
- Benchmark Problems for Phase Retrieval
- Adaptive Douglas--Rachford Splitting Algorithm for the Sum of Two Operators
- Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions
- On Alternating Direction Methods of Multipliers: A Historical Perspective
- Convergence Rate Analysis of Several Splitting Schemes
- The cyclic Douglas–Rachford algorithm with r-sets-Douglas–Rachford operators
- Searching with iterated maps
- Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
- A Douglas--Rachford Type Primal-Dual Method for Solving Inclusions with Mixtures of Composite and Parallel-Sum Type Monotone Operators
- Generalized Solutions for the Sum of Two Maximally Monotone Operators
- Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping
- On the Finite Convergence of the Douglas--Rachford Algorithm for Solving (Not Necessarily Convex) Feasibility Problems in Euclidean Spaces
- Convex analysis and monotone operator theory in Hilbert spaces
- On the maximality of the sum of two maximal monotone operators
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