The Splitting Algorithms by Ryu, by Malitsky–Tam, and by Campoy Applied to Normal Cones of Linear Subspaces Converge Strongly to the Projection onto the Intersection

DOI10.1137/22m1483165arXiv2203.03832OpenAlexW4380609297MaRDI QIDQ6158002

Shambhavi Singh, Shawn Xianfu Wang, Heinz H. Bauschke

Publication date: 22 June 2023

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

Full work available at URL: https://arxiv.org/abs/2203.03832

zbMATH Keywords

resolventnonexpansive mappingHilbert spacelinear convergencebest approximationmaximally monotone operatorintersection of subspacesCampoy splittingMalitsky-Tam splittingRyu splitting

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Monotone operators and generalizations (47H05) Numerical methods based on nonlinear programming (49M37) Best approximation, Chebyshev systems (41A50) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Decomposition methods (49M27) Applications of generalized inverses (15A10)

Related Items (2)

Regularity of sets under a reformulation in a product space with reduced dimension ⋮ Distributed forward-backward methods for ring networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces
• Generalized differentials of nonsmooth functions, and necessary conditions for an extremum
• Error bounds for the method of alternating projections
• On matrices having equal spectral radius and spectral norm
• Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm
• A product space reformulation with reduced dimension for splitting algorithms
• Uniqueness of DRS as the 2 operator resolvent-splitting and impossibility of 3 operator resolvent-splitting
• Strengthened splitting methods for computing resolvents
• The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
• Series and parallel addition of matrices
• The Douglas--Rachford Algorithm for Two (Not Necessarily Intersecting) Affine Subspaces
• The rate of convergence in the method of alternating projections
• Julia: A Fresh Approach to Numerical Computing
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Accelerating the convergence of the method of alternating projections
• Convex analysis and monotone operator theory in Hilbert spaces
• Best approximation in inner product spaces

This page was built for publication: The Splitting Algorithms by Ryu, by Malitsky–Tam, and by Campoy Applied to Normal Cones of Linear Subspaces Converge Strongly to the Projection onto the Intersection