The Douglas--Rachford Algorithm Converges Only Weakly

DOI10.1137/19M1308451zbMath1443.47058arXiv1912.09564OpenAlexW3020585756MaRDI QIDQ5107064

Patrick L. Combettes, Minh N. Bui

Publication date: 22 April 2020

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

Full work available at URL: https://arxiv.org/abs/1912.09564

zbMATH Keywords

strong convergenceweak convergencemonotone operatoroperator splittingDouglas-Rachford algorithmmethod of partial inverses

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (4)

Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists ⋮ Randomized Douglas–Rachford Methods for Linear Systems: Improved Accuracy and Efficiency ⋮ Resolvent and proximal compositions ⋮ Demiclosedness principles for generalized nonexpansive mappings

Cites Work

• Unnamed Item
• Partial inverse of a monotone operator
• An alternating projection that does not converge in norm
• On Weak Convergence of the Douglas–Rachford Method
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Convex analysis and monotone operator theory in Hilbert spaces

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