New Demiclosedness Principles for (Firmly) Nonexpansive Operators

DOI10.1007/978-1-4614-7621-4_2zbMath1297.47059arXiv1103.0991OpenAlexW1538512259MaRDI QIDQ5746429

Heinz H. Bauschke

Publication date: 18 February 2014

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.0991

zbMATH Keywords

resolventnonexpansive mappingmaximal monotone operatorsplitting algorithmproximal algorithmDouglas-Rachford algorithmfirmly nonexpansive mappingdemiclosedness principle

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15) Decomposition methods (49M27) Numerical methods for variational inequalities and related problems (65K15)

Related Items (8)

An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator ⋮ Parallel Normal S-Iteration Methods with Applications to Optimization Problems ⋮ The Douglas-Rachford algorithm for convex and nonconvex feasibility problems ⋮ Demiclosedness principles for generalized nonexpansive mappings ⋮ Attouch-Théra duality revisited: Paramonotonicity and operator splitting ⋮ The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle ⋮ Projective splitting methods for sums of maximal monotone operators with applications ⋮ On the finite termination of the Douglas-Rachford method for the convex feasibility problem

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