Dynamics of the Douglas-Rachford method for ellipses and \(p\)-spheres

DOI10.1007/s11228-017-0457-0OpenAlexW3099817079MaRDI QIDQ1653333

Anna Schneider, Scott B. Lindstrom, Matthew P. Skerritt, Jonathan M. Borwein, Brailey Sims

Publication date: 3 August 2018

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03975

zbMATH Keywords

iterative methodsdiscrete dynamical systemsfeasibilityDouglas-Rachfordprojection algorithms

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Nonlinear operators and their properties (47H99) Numerical aspects of recurrence relations (65Q30)

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Cites Work

• Unnamed Item
• Recent results on Douglas-Rachford methods for combinatorial optimization problems
• The Douglas-Rachford algorithm for the case of the sphere and the line
• Functional analysis, Sobolev spaces and partial differential equations
• Dynamics of the Douglas-Rachford method for ellipses and \(p\)-spheres
• The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
• On the Douglas-Rachford algorithm
• Global convergence of a non-convex Douglas-Rachford iteration
• The Douglas–Rachford Algorithm in the Absence of Convexity
• DOUGLAS–RACHFORD FEASIBILITY METHODS FOR MATRIX COMPLETION PROBLEMS
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Reflection Methods for Inverse Problems with Applications to Protein Conformation Determination
• Convex analysis and monotone operator theory in Hilbert spaces

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