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In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems.
T. Kose, “Solutions of saddle value problems by differential equations,” Econometrica, Journal of the Econometric Society , pp. 59–70, 1956
1956
Earlier work this paper cites.
K. J. Arrow, L. Hurwicz, and H. Uzawa, Studies in Linear and Nonlinear Programming . Stanford University Press, Palo Alto, 1958
1958
Earlier work this paper cites.
B. Polyak, “Iterative methods using Lagrange multipliers for solving extremal problems with constraints of the equation type,” USSR Computational Mathematics and Mathematical Physics , vol. 10, no. 5, pp. 42–52, 1970
1970
Earlier work this paper cites.
G. H. Chen and R. T. Rockafellar, “Convergence rates in forward–backward splitting,” SIAM Journal on Optimization , vol. 7, no. 2, pp. 421–444, 1997
1997
Earlier work this paper cites.
M. Kallio and C. H. Rosa, “Large-scale convex optimization via saddle point computation,” Operations Research , vol. 47, no. 1, pp. 93–101, 1999
1999
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, Convex Optimization . Cambridge University Press, 2004
2004
Earlier work this paper cites.
A. J. Laub, Matrix Analysis For Scientists And Engineers . SIAM, PA, USA, 2004
2004
Earlier work this paper cites.
A. Nedic and A. Ozdaglar, “Subgradient methods for saddle-point problems,” Journal of Optimization Theory and Applications , vol. 142, no. 1, pp. 205–228, 2009
2009
Earlier work this paper cites.
D. Feijer and F. Paganini, “Stability of primal–dual gradient dynamics and applications to network optimization,” Automatica , vol. 46, no. 12, pp. 1974–1981, 2010
2010
Earlier work this paper cites.
J. Wang and N. Elia, “A control perspective for centralized and distributed convex optimization,” in 50th IEEE conference on decision and control and European control conference , Orlando, FL, USA, Dec. 2011, pp. 3800–3805
2011
Earlier work this paper cites.
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces . Springer, 2011, vol. 408
2011
Earlier work this paper cites.
J. Chen and V. K. Lau, “Convergence analysis of saddle point problems in time varying wireless systems—control theoretical approach,” IEEE Transactions on Signal Processing , vol. 60, no. 1, pp. 443–452, 2012
2012
Earlier work this paper cites.
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course . Springer, 2013, vol. 87
2013
Earlier work this paper cites.
D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods . Academic press, 2014
2014
Cited alongside, same era.
W. Shi, Q. Ling, K. Yuan, G. Wu, and W. Yin, “On the linear convergence of the ADMM in decentralized consensus optimization,” IEEE Trans. Signal Process. , vol. 62, no. 7, pp. 1750–1761, 2014
2014
Cited alongside, same era.
A. H. Sayed, “Adaptation, learning, and optimization over neworks.” Foundations and Trends in Machine Learning , vol. 7, no. 4-5, pp. 311–801, 2014
2014
Cited alongside, same era.
S. V. Macua, J. Chen, S. Zazo, and A. H. Sayed, “Distributed policy evaluation under multiple behavior strategies,” IEEE Transactions on Automatic Control , vol. 60, no. 5, pp. 1260–1274, 2015
2015
Cited alongside, same era.
R. I. Bot, E. R. Csetnek, A. Heinrich, and C. Hendrich, “On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems,” Mathematical Programming , vol. 150, no. 2, pp. 251–279, 2015
A. Chambolle and T. Pock, “On the ergodic convergence rates of a first-order primal–dual algorithm,” Mathematical Programming , vol. 159, no. 1-2, pp. 253–287, Sept. 2016
2016
Later among the works it cites.
A. Mokhtari and A. Ribeiro, “DSA: Decentralized double stochastic averaging gradient algorithm,” Journal of Machine Learning Research (JMLR) , vol. 17, no. 1, pp. 2165–2199, 2016
2016
Later among the works it cites.
D. Davis and W. Yin, “A three-operator splitting scheme and its optimization applications,” Set-Valued and Variational Analysis , vol. 25, no. 4, pp. 829–858, Dec 2017
2017
Later among the works it cites.
A. Nedic, A. Olshevsky, and W. Shi, “Achieving geometric convergence for distributed optimization over time-varying graphs,” SIAM Journal on Optimization , vol. 27, no. 4, pp. 2597–2633, 2017
2017
Later among the works it cites.
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2015
Cited alongside, same era.
Q. Ling, W. Shi, G. Wu, and A. Ribeiro, “DLM: Decentralized linearized alternating direction method of multipliers,” IEEE Transactions on Signal Processing , vol. 63, pp. 4051–4064, 2015
2015
Cited alongside, same era.
T.-H. Chang, M. Hong, and X. Wang, “Multi-agent distributed optimization via inexact consensus ADMM,” IEEE Transactions on Signal Processing , vol. 63, no. 2, pp. 482–497, Jan. 2015
2015
Cited alongside, same era.
Z. J. Towfic and A. H. Sayed, “Stability and performance limits of adaptive primal-dual networks,” IEEE Trans. Signal Process. , vol. 63, no. 11, pp. 2888–2903, 2015
2015
Cited alongside, same era.
N. Komodakis and J.-C. Pesquet, “Playing with duality: An overview of recent primal-dual approaches for solving large-scale optimization problems,” IEEE Signal Processing Magazine , vol. 32, no. 6, pp. 31–54, 2015
2015
Cited alongside, same era.
W. Shi, Q. Ling, G. Wu, and W. Yin, “EXTRA: An exact first-order algorithm for decentralized consensus optimization,” SIAM Journal on Optimization , vol. 25, no. 2, pp. 944–966, 2015
2015
Cited alongside, same era.
A. Cherukuri and J. Cortes, “Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment,” Automatica , vol. 74, pp. 183–193, 2016
2016
Cited alongside, same era.
A. Cherukuri, E. Mallada, and J. Cortes, “Asymptotic convergence of constrained primal–dual dynamics,” Systems & Control Letters , vol. 87, pp. 10–15, 2016
2016
Cited alongside, same era.
J. Cortes and S. K. Niederlander, “Distributed coordination for nonsmooth convex optimization via saddle-point dynamics,” Journal of Nonlinear Science , vol. 29, no. 4, pp. 1247–1272, Aug 2019
2019
Closest in time.
N. K. Dhingra, S. Z. Khong, and M. R. Jovanovic, “The proximal augmented Lagrangian method for nonsmooth composite optimization,” IEEE Transactions on Automatic Control , vol. 64, no. 7, pp. 2861–2868, July 2019
2019
Closest in time.
G. Qu and N. Li, “On the exponential stability of primal-dual gradient dynamics,” IEEE Control Systems Letters , vol. 3, no. 1, pp. 43–48, Jan. 2019
2019
Closest in time.
S. S. Du and W. Hu, “Linear convergence of the primal-dual gradient method for convex-concave saddle point problems without strong convexity,” in Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) , Naha, Okinawa, Japan, April 2019, pp. 196–205
2019
Closest in time.
K. Yuan, B. Ying, X. Zhao, and A. H. Sayed, “Exact diffusion for distributed optimization and learning-Part I: Algorithm development,” IEEE Transactions on Signal Processing , vol. 67, no. 3, pp. 708–723, Feb. 2019
2019
Closest in time.
D. Jakovetic, “A unification and generalization of exact distributed first-order methods,” IEEE Transactions on Signal and Information Processing over Networks , vol. 5, no. 1, pp. 31–46, 2019
2019
Closest in time.
K. Yuan, B. Ying, X. Zhao, and A. H. Sayed, “Exact diffusion for distributed optimization and learning-Part II: Convergence analysis,” IEEE Transactions on Signal Processing , vol. 67, no. 3, pp. 724–739, Feb. 2019
2019
Closest in time.
S. A. Alghunaim, E. K. Ryu, K. Yuan, and A. H. Sayed, “Decentralized proximal gradient algorithms with linear convergence rates,” arXiv preprint:1909.06479 , Sept. 2019
2019
Closest in time.