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Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions.
Regularisation d’inequations variationelles par approximations successives
Martinet, B · 1970
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The extragradient method for finding saddle points and other problems
Korpelevich, G. M · 1976
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Monotone operators and the proximal point algorithm
Rockafellar, R. T · 1976
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A modification of the arrow-hurwicz method for search of saddle points
Popov, L. D · 1980
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Splitting methods for monotone operators with applications to parallel optimization
Eckstein, J · 1989
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On the douglas—rachford splitting method and the proximal point algorithm for maximal monotone operators
Eckstein, J. and Bertsekas, D. P · 1992
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Local convergence of the proximal point algorithm and multiplier methods without monotonicity
Pennanen, T · 2002
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Inexact variants of the proximal point algorithm without monotonicity
Iusem, A. N., Pennanen, T., and Svaiter, B. F · 2003
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Prox-method with rate of convergence O ( 1 / t ) (1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Nemirovski, A · 2004
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Robust optimization
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Learning multiple layers of features from tiny images
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Tight last-iterate convergence rates for no-regret learning in multi-player games
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Convex analysis and monotone operator theory in Hilbert spaces , volume 408
Bauschke, H. H., Combettes, P. L., et al · 2011
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Performance of first-order methods for smooth convex minimization: a novel approach
Drori, Y. and Teboulle, M · 2014
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Generative adversarial nets
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y · 2014
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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On the convergence rate of douglas–rachford operator splitting method
He, B. and Yuan, X · 2015
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Linear convergence and metric selection for douglas-rachford splitting and admm
Giselsson, P. and Boyd, S · 2016
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Improved training of wasserstein gans
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