Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm

DOI10.1007/s10957-019-01481-3zbMath1481.47080arXiv1805.09720OpenAlexW2803526611WikidataQ128492947 ScholiaQ128492947MaRDI QIDQ2420809

Francisco J. Aragón Artacho, Rubén Campoy

Publication date: 7 June 2019

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.09720

zbMATH Keywords

resolventstrong convergencesplitting methodmaximally monotone operatorDouglas-Rachford algorithmaveraged alternating modified reflections algorithm

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (7)

A product space reformulation with reduced dimension for splitting algorithms ⋮ Backward-forward-reflected-backward splitting for three operator monotone inclusions ⋮ Computing the resolvent of the sum of operators with application to best approximation problems ⋮ Strengthened splitting methods for computing resolvents ⋮ Iterative methods for computing the resolvent of the sum of a maximal monotone operator and composite operator with applications ⋮ SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD ⋮ On a decomposition formula for the resolvent operator of the sum of two set-valued maps with monotonicity assumptions

Cites Work

• Unnamed Item
• Unnamed Item
• Proximity for sums of composite functions
• A new projection method for finding the closest point in the intersection of convex sets
• Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm
• Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces
• On the Douglas-Rachford algorithm
• A theorem on maximal monotonic sets in Hilbert space
• On Weak Convergence of the Douglas–Rachford Method
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Decomposition through formalization in a product space
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• On a decomposition formula for the proximal operator of the sum of two convex functions
• Generalized Solutions for the Sum of Two Maximally Monotone Operators
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm