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Recently, the forward-backward and Douglas-Rachford envelope functions were proposed in the literature.
Functional Operators. Volume II. The Geometry of Orthogonal Spaces
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Finding the common point of convex sets by the method of successive projection
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Convex Analysis
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Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problémes de dirichlet non linéaires
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Splitting algorithms for the sum of two nonlinear operators
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D. Gabay · 1983
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Splitting methods for monotone operators with applications to parallel optimization
J. Eckstein · 1989
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Variational Analysis
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Preconditioning techniques for large linear systems: A survey
M. Benzi · 2002
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A first-order primal-dual algorithm for convex problems with applications to imaging
A. Chambolle and T. Pock · 2011
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The method of alternating relaxed projections for two nonconvex sets
H. H. Bauschke, H. M. Phan, and X. Wang · 2014
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Douglas-Rachford splitting: Complexity estimates and accelerated variants
P. Patrinos, L. Stella, and A. Bemporad · 2014
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Forward-backward truncated Newton methods for convex composite optimization
P. Patrinos, L. Stella, and A. Bemporad · 2014
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A three-operator splitting scheme and its optimization applications
D. Davis and W. Yin · 2015
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Introductory Lectures on Convex Optimization: A Basic Course
Y. Nesterov · 2003
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Solving monotone inclusions via compositions of nonexpansive averaged operators
P. L. Combettes · 2004
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Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems
Q. Hu and J. Zou · 2006
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Numerical optimization
J. Nocedal and S. Wright · 2006
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
H. H. Bauschke and P. L. Combettes · 2011
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Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Optimal parameter selection for the alternating direction method of multipliers (ADMM): Quadratic problems
E. Ghadimi, A. Teixeira, I. Shames, and M. Johansson · 2015
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Tight global linear convergence rate bounds for Douglas-Rachford splitting
P. Giselsson · 2015
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Metric selection in fast dual forward-backward splitting
P. Giselsson and S. Boyd · 2015
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Line search for averaged operator iteration
P. Giselsson, M. Fält, and S. Boyd · 2016
Closest in time.
Forward-backward quasi-Newton methods for nonsmooth optimization problems
L. Stella, A. Themelis, and P. Patrinos · 2016
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Linear convergence and metric selection for Douglas-Rachford splitting and ADMM
P. Giselsson and S. Boyd · 2017
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