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The Past Extragradient (PEG) [Popov, 1980] method, also known as the Optimistic Gradient method, has known a recent gain in interest in the optimization community with the emergence of variational inequality formulations for machine learning.
Fixed points of nonexpanding maps
B. Halpern · 1967
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The extragradient method for finding saddle points and other problems
G. M. Korpelevich · 1976
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A modification of the arrow-hurwicz method for search of saddle points
L. D. Popov · 1980
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An approach to obtaining global extremums in polynomial mathematical programming problems
N. Z. Shor · 1987
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On linear convergence of iterative methods for the variational inequality problem
P. Tseng · 1995
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Using sedumi 1.02, a MATLAB toolbox for optimization over symmetric cones
J. F. Sturm · 1999
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Squared functional systems and optimization problems
Y. Nesterov · 2000
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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
P. A. Parrilo · 2000
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Global optimization with polynomials and the problem of moments
J. B. Lasserre · 2001
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Finite-dimensional variational inequalities and complementarity problems
F. Facchinei and J.-S. Pang · 2003
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Yalmip: A toolbox for modeling and optimization in matlab
J. Lofberg · 2004
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Dual extrapolation and its applications to solving variational inequalities and related problems
Y. Nesterov · 2007
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Robust optimization
A. Ben-Tal, L. El Ghaoui, and A. Nemirovski · 2009
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Tight last-iterate convergence rates for no-regret learning in multi-player games
N. Golowich, S. Pattathil, and C. Daskalakis · 2010
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The MOSEK optimization software, 2010
A. Mosek · 2010
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Pid design by convex-concave optimization
M. Hast, K. J. Åström, B. Bernhardsson, and S. Boyd · 2013
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Performance of first-order methods for smooth convex minimization: a novel approach
Y. Drori and M. Teboulle · 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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Explaining and harnessing adversarial examples
I. J. Goodfellow, J. Shlens, and C. Szegedy · 2015
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Exact algorithms for linear matrix inequalities
D. Henrion, S. Naldi, and M. S. El Din · 2016
Cited alongside, same era.
On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
E. De Klerk, F. Glineur, and A. B. Taylor · 2017
Cited alongside, same era.
A. Mokhtari, A. Ozdaglar, and S. Pattathil · 2019
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Halpern iteration for near-optimal and parameter-free monotone inclusion and strong solutions to variational inequalities
J. Diakonikolas · 2020
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Stochastic hamiltonian gradient methods for smooth games
N. Loizou, H. Berard, A. Jolicoeur-Martineau, P. Vincent, S. Lacoste-Julien, and I. Mitliagkas · 2020
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Training gans with centripetal acceleration
W. Peng, Y.-H. Dai, H. Zhang, and L. Cheng · 2020
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Operator splitting performance estimation: Tight contraction factors and optimal parameter selection
E. K. Ryu, A. B. Taylor, C. Bergeling, and P. Giselsson · 2020
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Performance estimation toolbox (pesto): automated worst-case analysis of first-order optimization methods
A. B. Taylor, J. M. Hendrickx, and F. Glineur · 2017
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Training gans with optimism
C. Daskalakis, A. Ilyas, V. Syrgkanis, and H. Zeng · 2018
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Towards deep learning models resistant to adversarial attacks
A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu · 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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Solving imperfect-information games via discounted regret minimization
N. Brown and T. Sandholm · 2019
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Stable-predictive optimistic counterfactual regret minimization
G. Farina, C. Kroer, N. Brown, and T. Sandholm · 2019
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Convergence of gradient methods on bilinear zero-sum games
G. Zhang and Y. Yu · 2020
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E. Gorbunov, N. Loizou, and G. Gidel · 2021
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Fast extra gradient methods for smooth structured nonconvex-nonconcave minimax problems
S. Lee and D. Kim · 2021
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Halpern-type accelerated and splitting algorithms for monotone inclusions
Q. Tran-Dinh and Y. Luo · 2021
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Accelerated algorithms for smooth convex-concave minimax problems with O ( 1 / k 2 ) (1/k^{2}) rate on squared gradient norm
T. Yoon and E. K. Ryu · 2021
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On last-iterate convergence beyond zero-sum games
I. Anagnostides, I. Panageas, G. Farina, and T. Sandholm · 2022
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Y. Cai, A. Oikonomou, and W. Zheng · 2022
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Pepit: computer-assisted worst-case analyses of first-order optimization methods in python
B. Goujaud, C. Moucer, F. Glineur, J. Hendrickx, A. Taylor, and A. Dieuleveut · 2022
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The connection between nesterov’s accelerated methods and halpern fixed-point iterations
Q. Tran-Dinh · 2022
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