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Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces.
Proceedings of the American Mathematical Society 4
Mann, W.R.: Mean value methods in iteration · 1953
Earlier work this paper cites.
Uspekhi Matematicheskikh Nauk 10
Krasnosel’skiĭ, M.A.: Two remarks on the method of successive approximations · 1955
Earlier work this paper cites.
Courier Dover Publications (1956)
Knopp, K.: Infinite sequences and series · 1956
Earlier work this paper cites.
Bulletin of the American Mathematical Society 72
Browder, F.E., Petryshyn, W.: The solution by iteration of nonlinear functional equations in banach spaces · 1966
Earlier work this paper cites.
Rev. Francaise dAut. Inf. Rech. Oper R-2
Glowinski, R., Marrocco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet nonlinéaires · 1975
Earlier work this paper cites.
Computers & Mathematics with Applications 2
Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation · 1976
Earlier work this paper cites.
Israel Journal of Mathematics 29
Brézis, H., Lions, P.: Produits infinis de résolvantes · 1978
Earlier work this paper cites.
Studies in mathematics and its applications 15
Gabay, D.: Chapter ix applications of the method of multipliers to variational inequalities · 1983
Earlier work this paper cites.
Nemirovsky, A., Yudin, D.: Problem complexity and method efficiency in optimization. 1983
1983
Earlier work this paper cites.
Journal of mathematical analysis and applications 114
Franchetti, C., Light, W.: On the von Neumann alternating algorithm in hilbert space · 1986
Earlier work this paper cites.
Prentice-Hall, Inc. (1989)
Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and distributed computation: numerical methods · 1989
Earlier work this paper cites.
SIAM Journal on Control and Optimization 29
Güler, O.: On the Convergence of the Proximal Point Algorithm for Convex Minimization · 1991
Earlier work this paper cites.
Mathematical Programming 55
Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators · 1992
Earlier work this paper cites.
Studies in Computational Mathematics 8
Combettes, P.L.: Quasi-Fejérian analysis of some optimization algorithms · 2001
Earlier work this paper cites.
Numerical Functional Analysis and Optimization 23
Ogura, N., Yamada, I.: Non-strictly convex minimization over the fixed point set of an asymptotically shrinking nonexpansive mapping · 2002
Earlier work this paper cites.
Optimization 53
Combettes, P.L.: Solving monotone inclusions via compositions of nonexpansive averaged operators · 2004
Cited alongside, same era.
Springer (2004)
Nesterov, Y.: Introductory lectures on convex optimization: A basic course, vol. 87 · 2004
Cited alongside, same era.
Signal Processing, IEEE Transactions on 56
Schizas, I.D., Ribeiro, A., Giannakis, G.B.: Consensus in ad hoc wsns with noisy linksÑpart i: Distributed estimation of deterministic signals · 2008
Cited alongside, same era.
International Transactions in Operational Research 16
Bauschke, H.H., Deutsch, F., Hundal, H.: Characterizing arbitrarily slow convergence in the method of alternating projections · 2009
Cited alongside, same era.
SIAM Journal on Imaging Sciences 2
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems · 2009
Cited alongside, same era.
Inverse Problems 25
Bredies, K.: A forward–backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space · 2009
arXiv preprint arXiv:1212.5942 (2012)
Briceño-Arias, L.M.: Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions · 2012
Later among the works it cites.
Tech. rep. (2012)
He, B., Yuan, X.: On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers · 2012
Later among the works it cites.
SIAM Journal on Numerical Analysis 50
He, B., Yuan, X.: On the O ( 1 / n ) O(1/n) convergence rate of the Douglas-Rachford alternating direction method · 2012
Later among the works it cites.
In: Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, pp. 5445–5450. IEEE (2012)
Wei, E., Ozdaglar, A.: Distributed alternating direction method of multipliers · 2012
Later among the works it cites.
arXiv preprint arXiv:1309.5548 (2013)
Chen, Y., Lan, G., Ouyang, Y.: Optimal primal-dual methods for a class of saddle point problems · 2013
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Cited alongside, same era.
SIAM Journal on Imaging Sciences 2
Goldstein, T., Osher, S.: The split Bregman method for l1-regularized problems · 2009
Cited alongside, same era.
Optimization for Machine Learning 2010
Bertsekas, D.P.: Incremental gradient, subgradient, and proximal methods for convex optimization: A survey · 2010
Cited alongside, same era.
SIAM Journal on Optimization 20
Monteiro, R.D.C., Svaiter, B.F.: On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean · 2010
Cited alongside, same era.
Springer (2011)
Bauschke, H.H., Combettes, P.L.: Convex analysis and monotone operator theory in Hilbert spaces · 2011
Cited alongside, same era.
Foundations and Trends in Machine Learning 3
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers · 2011
Cited alongside, same era.
Journal of Mathematical Imaging and Vision 40
Chambolle, A., Pock, T.: A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging · 2011
Cited alongside, same era.
Later among the works it cites.
Journal of Optimization Theory and Applications 158
Condat, L.: A primal–dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms · 2013
Later among the works it cites.
arXiv preprint arXiv:1312.3040 (2013)
Deng, W., Lai, M.J., Yin, W.: On the o ( 1 / k ) o(1/k) convergence and parallelization of the alternating direction method of multipliers · 2013
Later among the works it cites.
SIAM Journal on Optimization 23
Monteiro, R.D., Svaiter, B.F.: Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers · 2013
Later among the works it cites.
arXiv preprint arXiv:1307.5561 (2013)
Shi, W., Ling, Q., Yuan, K., Wu, G., Yin, W.: On the linear convergence of the ADMM in decentralized consensus optimization · 2013
Later among the works it cites.
Advances in Computational Mathematics 38
Vũ, B.C.: A splitting algorithm for dual monotone inclusions involving cocoercive operators · 2013
Later among the works it cites.
Journal of Approximation Theory 185
Bauschke, H.H., Bello Cruz, J.Y., Nghia, T.T.A., Phan, H.M., Wang, X.: The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the friedrichs angle · 2014
Closest in time.
SIAM Journal on Optimization 24
Corman, E., Yuan, X.: A Generalized Proximal Point Algorithm and Its Convergence Rate · 2014
Closest in time.
arXiv preprint arXiv:1404.4837 (2014)
Liang, J., Fadili, J., Peyré, G.: Convergence rates with inexact nonexpansive operators · 2014
Closest in time.
SIAM Journal on Optimization 24
Shefi, R., Teboulle, M.: Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization · 2014
Closest in time.