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This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems.
A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach
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Proximal point approximations achieving a convergence rate of o(1/k) for smooth convex-concave saddle point problems: Optimistic gradient and extra-gradient methods
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On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
R. D. C. Monteiro and B. F. Svaiter · 2010
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Complexity of variants of tseng’s modified fb splitting and korpelevich’s methods for hemivariational inequalities with applications to saddle-point and convex optimization problems
R. D. C. Monteiro and B. F. Svaiter · 2011
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Accelerated primal-dual proximal block coordinate updating methods for constrained convex optimization
Y. Xu and S. Zhang · 2018
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Stabilizing adversarial nets with prediction methods
A. Yadav, S. Shah, Z. Xu, D. Jacobs, and T. Goldstein · 2018
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Last-iterate convergence rates for min-max optimization
J. Abernethy, K. A. Lai, and A. Wibisono · 2019
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Accelerated methods for composite non-bilinear saddle point problem
M. Alkousa, D. Dvinskikh, F. Stonyakin, and A. Gasnikov · 2019
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Reducing noise in GAN training with variance reduced extragradient
T. Chavdarova, G. Gidel, F. Fleuret, and S. Lacoste-Julien · 2019
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Stochastic model-based minimization of weakly convex functions
D. Davis and D. Drusvyatskiy · 2019
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Statistical Decision Theory and Bayesian Analysis
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Y. Nesterov · 2013
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Optimal primal-dual methods for a class of saddle point problems
Y. Chen, G. Lan, and Y. Ouyang · 2014
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Fast alternating direction optimization methods
T. Goldstein, B. O’Donoghue, S. Setzer, and R. Baraniuk · 2014
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Generative adversarial nets
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Projected reflected gradient methods for monotone variational inequalities
Y. Malitsky · 2015
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An accelerated linearized alternating direction method of multipliers
Y. Ouyang, Y. Chen, G. Lan, and E. Pasiliao Jr · 2015
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A variational inequality perspective on generative adversarial networks
G. Gidel, H. Berard, G. Vignoud, P. Vincent, and S. Lacoste-Julien · 2019
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On the convergence of single-call stochastic extra-gradient methods
Y-G. Hsieh, F. Iutzeler, J. Malick, and P. Mertikopoulos · 2019
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Lower bounds and conditioning of differentiable games
A. Ibrahim, W. Azizian, G. Gidel, and I. Mitliagkas · 2019
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Minmax optimization: Stable limit points of gradient descent ascent are locally optimal
C. Jin, P. Netrapalli, and M. I. Jordan · 2019
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An accelerated inexact proximal point method for solving nonconvex-concave min-max problems
W. Kong and R. D. C. Monteiro · 2019
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Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks
T. Liang and J. Stokes · 2019
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On gradient descent ascent for nonconvex-concave minimax problems
T. Lin, C. Jin, and M. I. Jordan · 2019
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Hybrid block successive approximation for one-sided non-convex min-max problems: algorithms and applications
S. Lu, I. Tsaknakis, M. Hong, and Y. Chen · 2019
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Optimistic mirror descent in saddle-point problems: Going the extra(-gradient) mile
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Revisiting stochastic extragradient
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Solving a class of non-convex min-max games using iterative first order methods
M. Nouiehed, M. Sanjabi, T. Huang, J. D. Lee, and M. Razaviyayn · 2019
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Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems
Y. Ouyang and Y. Xu · 2019
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Efficient algorithms for smooth minimax optimization
K. K. Thekumparampil, P. Jain, P. Netrapalli, and S. Oh · 2019
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Accelerated primal dual method for a class of saddle point problem with strongly convex component
Z. Xie and J. Shi · 2019
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Iteration complexity of inexact augmented lagrangian methods for constrained convex programming
Y. Xu · 2019
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On lower iteration complexity bounds for the saddle point problems
J. Zhang, M. Hong, and S. Zhang · 2019
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Optimal algorithms for stochastic three-composite convex-concave saddle point problems
R. Zhao · 2019
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Accelerating smooth games by manipulating spectral shapes
W. Azizian, D. Scieur, I. Mitliagkas, S. Lacoste-Julien, and G. Gidel · 2020
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Efficient search of first-order nash equilibria in nonconvex-concave smooth min-max problems
D. M. Ostrovskii, A. Lowy, and M. Razaviyayn · 2020
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A primal dual smoothing framework for max-structured nonconvex optimization
R. Zhao · 2020
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