Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems

DOI10.1007/s10898-018-0654-xzbMath1499.90170arXiv1710.09814OpenAlexW2796899174WikidataQ129973878 ScholiaQ129973878MaRDI QIDQ1630271

Minh N. Dao, Hung M. Phan

Publication date: 7 December 2018

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.09814

zbMATH Keywords

linear convergencestrong regularitycyclic algorithmsuperregularitylinear regularityaffine-hull regularitygeneralized Douglas-Rachford algorithmquasi coercivityquasi Fejér monotonicity

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) Iterative procedures involving nonlinear operators (47J25) Decomposition methods (49M27)

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Cites Work

• Unnamed Item
• Unnamed Item
• On local convergence of the method of alternating projections
• On Slater's condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces
• Restricted normal cones and the method of alternating projections: applications
• Restricted normal cones and the method of alternating projections: theory
• Linear and strong convergence of algorithms involving averaged nonexpansive operators
• The method of alternating relaxed projections for two nonconvex sets
• Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
• Local linear convergence for alternating and averaged nonconvex projections
• Transversality and alternating projections for nonconvex sets
• Remarks on piecewise-linear algebra
• Dykstra's alternating projection algorithm for two sets
• The Douglas-Rachford algorithm in the affine-convex case
• Strong conical hull intersection property, bounded linear regularity, Jameson's property \((G)\), and error bounds in convex optimization
• 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
• On the Douglas-Rachford algorithm
• About regularity of collections of sets
• Linear convergence of the Douglas–Rachford method for two closed sets
• Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study
• On Weak Convergence of the Douglas–Rachford Method
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Some continuity properties of polyhedral multifunctions
• Variational Analysis
• On Projection Algorithms for Solving Convex Feasibility Problems
• Norm convergence of realistic projection and reflection methods
• Searching with iterated maps
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• 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