References
- Bruckstein AM, Donoho DL, Elad M. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 2009;51:34–81.
- Douglas J, Rachford HH. On the numerical solution of heat conduction problems in two or three space variables. Trans Am Math Soc. 1956;82:421–439.
- Lions PL, Mercier B. Splitting algorithms for the sum of two nonlinear operators. SIAM J Numer Anal. 1979;16:964–979.
- Svaiter BF. On weak convergence of the Douglas-Rachford method. SIAM J Control Optim. 2011;49(1):280–287.
- Eckstein J, Bertsekas DP. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math Program. 1992;55:293–318.
- Lawrence J, Spingarn JE. On fixed points of nonexpansive piecewise isometric mappings. Proc Lond Math Soc. 1987;55(3):605–624.
- Gabay D. Application of the method of multipliers to variational inequalities. In: Fortin M, Glowinski, R, editors. Augmented Lagrangian methods: application to the numerical solution of boundary-value problem. Amsterdam: North-Holland; 1983. p. 299–331.
- Dao MN, Phan H. Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems. J Global Optim. 2018;72(3):443–474.
- He BS, Yuan XM. On the convergence rate of the Douglas-Rachford operator splitting method. Math Program. 2015;153:715–722.
- He BS, Yuan XM. On the O(1/n) convergence rate of the douglas-rachford alternating direction method. SIAM J Numer Anal. 2012;50(2):700–709.
- Phan HM. Linear convergence of the Douglas-Rachford method for two closed sets. Optimization. 2016;65(2):369–385.
- Bayram I, Selesnick IW. The Douglas-Rachford algorithm for weakly convex penalties. 2015. Preprint arXiv:1511.03920v1.
- Guo K, Han DR. A note on the Douglas-Rachford splitting method for optimization problems involving hypoconvex functions. J Glob Optim. 2018;72(3):431–441.
- Guo K, Han DR, Yuan XM. Convergence analysis of Douglas-Rachford splitting method for ‘strongly+weakly’ convex programming. SIAM J Numer Anal. 2017;55:1549–1577.
- Dao MN, Phan HM. Adaptive Douglas-Rachford splitting algorithm for the sum of two operators. SIAM J Optim. 2019;29(4):2697–2724.
- Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. Cham: Springer; 2017.
- Cegielski A. Application of quasi-nonexpansive operators to an iterative method for variational inequality. SIAM J Optim. 2015;25:2165–2181.
- Cegielski A, Reich S, Zalas R. Regular sequences of quasi-nonexpansive operators and their applications. SIAM J Optim. 2018;28:1508–1532.
- Krasnosel'skiĭ MA. Two remarks on the method of successive approximations. Uspekhi Mat Nauk. 1955;63:123–127.
- Kolobov VI, Reich S, Zalas R. Weak, strong, and linear convergence of a double-layer fixed point algorithm. SIAM J Optim. 2017;27(3):1431–1458.
- Mann WR. Mean value methods in iteration. Proc Am Math Soc. 1955;4:506–510.
- Baillon JB, Bruck RE. The rate of asymptotic regularity is O(1n). Lect Notes Pure Appl Math. 1996;178:51–81.
- Cominetti R, Soto JA, Vaisman J. On the rate of convergence of Krasnoselski-Mann iterations and their connection with sums of Bernoullis. Israel J Math. 2014;199(2):757–772.
- Liang J, Fadili J, Peyre G. Convergence rates with inexact non-expansive operators. Math Program. 2016;159(1–2):403–434.
- Bravo M, Cominetti R, Pavez-Signé M. Rates of convergence for inexact Krasnosel'skiĭ-Mann iterations in Banach spaces. Math Program. 2019;175(1-2):241–262.
- Boţ RI, Csetnek ER. A dynamical system associated with the fixed points set of a nonexpansive operator. J Dyn Differ Equ. 2017;29(1):155–168.
- Arrow K, Hurwicz L. Gradient methods for constrained maxima. Oper Res. 1957;5(2):258–265.
- Abbas B, Attouch H, Svaiter BF. Newton-like dynamics and forward-backward methods for structured monotone inclusions in Hilbert spaces. J Optim Theor Appl. 2014;161:331–360.
- Abbas B, Attouch H. Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator. Optimization. 2015;64:2223–2252.
- Attouch H, Svaiter BF. A continuous dynamical Newton-like approach to solving monotone inclusions. SIAM J Control Optim. 2011;49:574–598.
- Bolte J. Continuous gradient projection method in Hilbert spaces. J Optim Theory Appl. 2003;119:235–259.
- Boţ RI, Csetnek ER. Convergence rates for forward-backward dynamical systems associated with strongly monotone inclusions. J Math Anal Appl. 2018;457(2):1135–1152.
- Boţ RI, Csetnek ER. Second order forward-backward dynamical systems for monotone inclusion problems. SIAM J Control Optim. 2016;54(3):1423–1443.
- Csetnek ER, Malitsky Y, Tam MK. Shadow Douglas-Rachford splitting for monotone inclusions. Appl Math Optim. 2019;80(3):665–678.
- Zhu M, Hu R, Fang Y. A continuous dynamical splitting method for solving ‘strongly+weakly’ convex programming problems. Optimization. 2020;69(6):1335–1359.
- Rockafellar RT, Wets RJB. Variational analysis. Berlin: Springer; 2010.
- Borwein JM. Fifty years of maximal monotonicity. Optim Lett. 2010;4(4):473–490.
- Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. (French) North-Holland Mathematics Studies. Vol. 5, Notas de Matemática; Vol. 50, 1973.
- Haraux A, Jendoubi MA. The convergence problem for dissipative autonomous systems: classical methods and recent advances. Heidelberg: Springer; 2015.
- Dontchev AL, Rockafellar RT. Implicit functions and solution mappings. New York: Springer; 2009.
- Wang F, Xu HK. Cyclic algorithms for split feasibility problems in Hilbert spaces. Nonlinear Anal. 2011;74:4105–4111.
- Cegielski A. General method for solving the split common fixed point problem. J Optim Theory Appl. 2015;165:385–404.
- Teschl G. Ordinary differential equations and dynamical systems. Providence (RI): American Mathematical Society; 2012.
- Vial JP. Strong and weak convexity of sets and functions. Math Oper Res. 1983;8(2):231–259.
- Mordukhovich BS. Variational analysis and generalized differentiation I: basic theory. Springer: Berlin; 2006.