Norm convergence of realistic projection and reflection methods

DOI10.1080/02331934.2014.947499zbMath1440.47050arXiv1312.7323OpenAlexW1969274089MaRDI QIDQ4981851

Brailey Sims, Matthew K. Tam, Jonathan M. Borwein

Publication date: 20 March 2015

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7323

zbMATH Keywords

strong convergenceprojection methodsnorm convergenceDouglas-Rachford methodHilbert latticealternating projection methodreflection methods

Mathematics Subject Classification ID

Convex programming (90C25) Iterative procedures involving nonlinear operators (47J25) Programming in abstract spaces (90C48) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (9)

Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems ⋮ Regularity and stability for a convex feasibility problem ⋮ The Douglas-Rachford algorithm for convex and nonconvex feasibility problems ⋮ Convergence Rate Analysis for Averaged Fixed Point Iterations in Common Fixed Point Problems ⋮ A variational approach to the alternating projections method ⋮ Stability of a convex feasibility problem ⋮ Ergodic behaviour of a Douglas-Rachford operator away from the origin ⋮ SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD ⋮ Adaptive Douglas--Rachford Splitting Algorithm for the Sum of Two Operators

Cites Work

• Moreau's decomposition in Banach spaces
• Restricted normal cones and the method of alternating projections: theory
• Recent results on Douglas-Rachford methods for combinatorial optimization problems
• Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
• Local linear convergence for alternating and averaged nonconvex projections
• On the convergence of von Neumann's alternating projection algorithm for two sets
• An alternating projection that does not converge in norm
• 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
• Spokes, mirrors and alternating projections
• On the local convergence of the Douglas-Rachford algorithm
• DOUGLAS–RACHFORD FEASIBILITY METHODS FOR MATRIX COMPLETION PROBLEMS
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Continuity and Differentiability Properties of Convex Operators
• A new proximal point iteration that converges weakly but not in norm
• On Projection Algorithms for Solving Convex Feasibility Problems
• Searching with iterated maps
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Norm convergence of realistic projection and reflection methods