On the linear convergence of circumcentered isometry methods

DOI10.1007/s11075-020-00966-xOpenAlexW3041713322MaRDI QIDQ2021771

Hui Ouyang, Heinz H. Bauschke, Shawn Xianfu Wang

Publication date: 27 April 2021

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

Full work available at URL: https://arxiv.org/abs/1912.01063

zbMATH Keywords

isometrylinear convergenceprojectorFriedrichs anglemethod of alternating projectionsbest approximation problemreflectoraccelerated symmetric method of alternating projectionscircumcentered isometry methodcircumcentered reflection method

Mathematics Subject Classification ID

Convex programming (90C25) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Best approximation, Chebyshev systems (41A50) Isometric theory of Banach spaces (46B04) Operator theory (47-XX) Acceleration of convergence in numerical analysis (65B99)

Related Items

Circumcentering approximate reflections for solving the convex feasibility problem ⋮ Circumcentering reflection methods for nonconvex feasibility problems ⋮ Bregman circumcenters: basic theory ⋮ Circumcentric directions of cones ⋮ Bregman circumcenters: monotonicity and forward weak convergence ⋮ On the centralization of the circumcentered-reflection method ⋮ A successive centralized circumcentered-reflection method for the convex feasibility problem ⋮ Unnamed Item ⋮ The circumcentered-reflection method achieves better rates than alternating projections ⋮ Best approximation mappings in Hilbert spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Acceleration schemes for the method of alternating projections
• Circumcentering the Douglas-Rachford method
• The block-wise circumcentered-reflection method
• The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
• On the linear convergence of the circumcentered-reflection method
• On the circumcentered-reflection method for the convex feasibility problem
• Accelerating the convergence of the method of alternating projections
• On circumcenters of finite sets in Hilbert spaces
• The method of projections for finding the common point of convex sets
• Convex analysis and monotone operator theory in Hilbert spaces
• Best approximation in inner product spaces